{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "617fe864-a317-42a2-926e-544e96026286",
   "metadata": {},
   "source": [
    "# Filter Networks #\n",
    "\n",
    "### Approach ###\n",
    "\n",
    "Analysing simple RC networks for the purpose of producing phase shifts of sine waves which in turn might be useful later for producing oscillatory networks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "693e7655",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Image\n",
    "from sympy import Matrix, symbols, Symbol, init_printing, Function, dsolve, checkodesol, sin, cos,exp, pi, Eq, \\\n",
    "    solveset, collect, cancel, simplify, lambdify, acos, atan, sqrt, I, integrate, factor, factor_list, Matrix, expand, \\\n",
    "    conjugate, Rational, sympify\n",
    "import sympy\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.signal import  find_peaks\n",
    "from scipy.integrate import solve_ivp\n",
    "import numpy as np\n",
    "from sympy.abc import phi\n",
    "from functools import reduce\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "a16c4a3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "from sympy import Function, Equality, Mul, Add"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d8541032",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.13.1'"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from system_eqns import systemEqns\n",
    "import sympy \n",
    "sympy.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a699a5b",
   "metadata": {},
   "source": [
    "## The simplest RC network\n",
    "\n",
    "A network containing only one capacitor and resistor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "effe33dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://images.kiwiheretic.xyz/RC-filter0.jpg\" width=\"600\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(url='https://images.kiwiheretic.xyz/RC-filter0.jpg', width=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6057575f",
   "metadata": {},
   "source": [
    "This is the simplest RC filter I can think of.  It only contains one current path for $ \\textit{i} $.\n",
    "\n",
    "Therefore:\n",
    "\n",
    "$$ V_{in} = V_c + R \\textit{i} $$\n",
    "\n",
    "However $ \\textit{i} = C \\frac{d V_c}{dt} $ and we want to think about the case where $ V_{in} = A \\sin( 2 \\pi f t) $ and so we have:\n",
    "\n",
    "$$ A \\sin (2 \\pi f t ) = V_c(t) + R C \\frac{d V_c}{dt} $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "ec4b6463",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( V_{in}, \\  V_{c}, \\  C, \\  R, \\  i, \\  t, \\  f, \\  A, \\  \\tau, \\  \\omega\\right)$"
      ],
      "text/plain": [
       "(V_{in}, V_c, C, R, i, t, f, A, τ, ω)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vin, Vc, C, R, i, t, f, A, tau, w = symbols(\"V_{in} V_c C R i t f A tau omega\", real=True, positive=True)\n",
    "Vin, Vc, C, R, i, t, f, A, tau, w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "cd33a7be",
   "metadata": {},
   "outputs": [],
   "source": [
    "def multiplyIt(x, y):\n",
    "    return sympify(x)*sympify(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "aa2552f8-b13f-44dc-b39c-ceaaa24040b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def getSym(expr, symbolName):\n",
    "    for sym in expr.free_symbols:\n",
    "        if sym.name == symbolName:\n",
    "            return sym\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "0fb16257",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the voltage across the capacitor as a function of time\n",
    "VC = Function(\"V_c\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "2ff1f3dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define \"driving term\" of the differential equation\n",
    "dt =A*sin(2*pi*f*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "ba8ccfa4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle A \\sin{\\left(2 \\pi f t \\right)} = C R \\frac{d}{d t} V_{c}{\\left(t \\right)} + V_{c}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "                     d                  \n",
       "A⋅sin(2⋅π⋅f⋅t) = C⋅R⋅──(V_c(t)) + V_c(t)\n",
       "                     dt                 "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Present the differential equation of the circuit\n",
    "eqn1 = Eq(dt , VC(t) + R * C * VC(t).diff(t))\n",
    "eqn1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "d0b3ec67",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle V_{c}{\\left(t \\right)} = - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + C_{1} e^{- \\frac{t}{C R}}$"
      ],
      "text/plain": [
       "                                                 -t \n",
       "                                                 ───\n",
       "           A⋅C⋅R⋅ω⋅cos(ω⋅t)    A⋅sin(ω⋅t)        C⋅R\n",
       "V_c(t) = - ──────────────── + ──────────── + C₁⋅ℯ   \n",
       "              2  2  2          2  2  2              \n",
       "             C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1          "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solve for the voltage across the capacitor wrt time\n",
    "dsoln = dsolve(eqn1, VC(t)).subs(2*pi*f, w)\n",
    "dsoln"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "b6f3dac6-c950-48b4-bae6-c95b000191fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( C_{1} e^{- \\frac{t}{C R}}, \\  \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\  - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}\\right)$"
      ],
      "text/plain": [
       "⎛    -t                                   ⎞\n",
       "⎜    ───                                  ⎟\n",
       "⎜    C⋅R   A⋅sin(ω⋅t)   -A⋅C⋅R⋅ω⋅cos(ω⋅t) ⎟\n",
       "⎜C₁⋅ℯ   , ────────────, ──────────────────⎟\n",
       "⎜          2  2  2          2  2  2       ⎟\n",
       "⎝         C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1   ⎠"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "terms = dsoln.args[1].args\n",
    "terms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "c3b1ca2a-616a-4ab1-9be9-99d466fe848c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "exp"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(terms[0].args[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "cd43b477-21dd-4064-a5ad-ce4390806d3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "     A      \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "terms[1].coeff(sin(w*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "b5915fc9-dfc5-4da5-ae99-d51ee8009753",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sin"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(sin(w*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "c068c13d-9775-4e30-a283-66996e5db57f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{sin: 3}"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{ sin: 3 }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b5b073b5-e7db-4e75-aded-d8fa32a51d87",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "  A⋅C⋅R⋅ω⋅cos(ω⋅t)    A⋅sin(ω⋅t) \n",
       "- ──────────────── + ────────────\n",
       "     2  2  2          2  2  2    \n",
       "    C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nonTransient = sum(terms[1:])\n",
    "nonTransient"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a3c5e39",
   "metadata": {},
   "source": [
    "### Find value for $ C_1 $\n",
    "At this point we want to find $ C_1 $ by setting $ V_c(0) = 0 $.  This seems reasonable that the capacitor starts off with no charge on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a93838da",
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = Symbol('C1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e7608c5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1 in dsoln.free_symbols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "804836bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega}{C^{2} R^{2} \\omega^{2} + 1} + V_{c}{\\left(0 \\right)}$"
      ],
      "text/plain": [
       "  A⋅C⋅R⋅ω            \n",
       "──────────── + V_c(0)\n",
       " 2  2  2             \n",
       "C ⋅R ⋅ω  + 1         "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solve for C1\n",
    "c1eq = solveset(dsoln.subs([(t,0)]), c1).args[0]; c1eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "bc4fa20e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "  A⋅C⋅R⋅ω   \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We will assume VC = 0 at t = 0.  No charge on capacitor at start. \n",
    "c1eq.args[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e61d4d03",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + C_{1} e^{- \\frac{t}{C R}}$"
      ],
      "text/plain": [
       "                                        -t \n",
       "                                        ───\n",
       "  A⋅C⋅R⋅ω⋅cos(ω⋅t)    A⋅sin(ω⋅t)        C⋅R\n",
       "- ──────────────── + ──────────── + C₁⋅ℯ   \n",
       "     2  2  2          2  2  2              \n",
       "    C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1          "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn1 = dsoln.rhs; eqn1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2aa9fc95",
   "metadata": {},
   "source": [
    "At this point I am going to try and ignore the transient part of the solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8e6be21a-fffe-43c0-8f72-b8802214579a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "  A⋅C⋅R⋅ω⋅cos(ω⋅t)    A⋅sin(ω⋅t) \n",
       "- ──────────────── + ────────────\n",
       "     2  2  2          2  2  2    \n",
       "    C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nonTransient"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "544e0b9c-be81-4713-a933-18b10137b76f",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "### Computation of phase and magnitude \n",
    "\n",
    "We might like to find out the amplitude and phase of the above formula given that it has both a sin and cosine term in it.  The result will be a superposition which will have a different amplitude and phase of any of them separately.  \n",
    "\n",
    "If we remember that for $ C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta + \\alpha ) $.  The constants $ C_1, C_2 \\mathrm{and} C_3 $ have nothing to do with the constant of integration $ C_1 $ mentioned above.  It is simply because I am running out of meaningful variable names.\n",
    "\n",
    "Then:\n",
    "\n",
    "$$ C_3^2 = C_1^2 + C_2^2 $$\n",
    "\n",
    "and\n",
    "\n",
    "we can try to reduce this formula:\n",
    "\n",
    "$$ C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta + \\alpha ) $$\n",
    "$$ \\Rightarrow C_1 \\sin( \\theta ) + C_2 \\cos (\\theta) = C_3 * \\cos ( \\theta ) \\cos  (\\alpha ) - C_3 * \\sin ( \\theta ) \\sin  (\\alpha )  $$\n",
    "$$ \\Rightarrow C_1  =  C_3 * \\sin  (\\alpha ) \\textrm{ and } C_2  =  C_3 * \\cos  (\\alpha ) $$\n",
    "$$ \\Rightarrow \\tan( \\alpha ) = C_1 / C_2 $$\n",
    "$$ \\Rightarrow \\tan^2( \\alpha ) = C_1^2 / C_2^2 $$\n",
    "$$ \\Rightarrow \\tan^2( \\alpha ) + 1 = C_1^2 / C_2^2 + C_2^2/C_2^2 =\\frac{C_1^2 + C_2^2}{C_2^2} $$\n",
    "$$ \\Rightarrow \\cos^2( \\alpha ) = \\frac{C_2^2}{C_1^2 + C_2^2}  $$\n",
    "$$ \\Rightarrow \\alpha = \\cos^{-1} \\left( \\sqrt {\\frac{ C_2^2 } { C_1^2 + C_2^2 }} \\right)  $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5750b889-b0d4-4def-b879-7de0b4f15a12",
   "metadata": {},
   "source": [
    "### Compute V_out "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9d2e8ec0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega \\left(C R \\omega \\sin{\\left(\\omega t \\right)} + \\cos{\\left(\\omega t \\right)}\\right)}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "A⋅C⋅R⋅ω⋅(C⋅R⋅ω⋅sin(ω⋅t) + cos(ω⋅t))\n",
       "───────────────────────────────────\n",
       "            2  2  2                \n",
       "           C ⋅R ⋅ω  + 1            "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the voltage at the output\n",
    "vout = simplify(A * sin(w*t) - nonTransient)\n",
    "vout"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "96b9d83f-50e8-4974-b9bd-be0e4e0e6b17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "   2  2  2                            \n",
       "A⋅C ⋅R ⋅ω ⋅sin(ω⋅t)   A⋅C⋅R⋅ω⋅cos(ω⋅t)\n",
       "─────────────────── + ────────────────\n",
       "    2  2  2              2  2  2      \n",
       "   C ⋅R ⋅ω  + 1         C ⋅R ⋅ω  + 1  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vrsterms = expand(vout)\n",
    "vrsterms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f64e2cea-1fbf-4842-bda5-a1d2e7d5fd6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\  \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}\\right)$"
      ],
      "text/plain": [
       "⎛                     2  2  2         ⎞\n",
       "⎜A⋅C⋅R⋅ω⋅cos(ω⋅t)  A⋅C ⋅R ⋅ω ⋅sin(ω⋅t)⎟\n",
       "⎜────────────────, ───────────────────⎟\n",
       "⎜   2  2  2            2  2  2        ⎟\n",
       "⎝  C ⋅R ⋅ω  + 1       C ⋅R ⋅ω  + 1    ⎠"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vrstermslist = vrsterms.args\n",
    "vrstermslist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "fdd288fe-941d-42f7-bc45-2dd64c7cfcb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "  A⋅C⋅R⋅ω   \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get cosine coefficient\n",
    "coscf = reduce(multiplyIt, (filter(lambda x:type(x) not in [cos],vrstermslist[0].args)))\n",
    "coscf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "653a6ade-b6ed-4039-a3e0-a2d9be144ce2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "    2  2  2 \n",
       " A⋅C ⋅R ⋅ω  \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get cosine coefficient\n",
    "sincf = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],vrstermslist[1].args)))\n",
    "sincf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1833b696",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A^{2} C^{2} R^{2} \\omega^{2}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       " 2  2  2  2 \n",
       "A ⋅C ⋅R ⋅ω  \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c3_2 = simplify(sincf**2 + coscf**2)\n",
    "c3_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e441c722",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(C R \\omega \\right)}$"
      ],
      "text/plain": [
       "atan(C⋅R⋅ω)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now compute the phase shift at the output\n",
    "alpha = atan(sincf/coscf)\n",
    "alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68fba51d",
   "metadata": {},
   "source": [
    "### Find magnitude of voltage across $ V_c $ and phase shift ###\n",
    "\n",
    "The phase shift is in relation to the input voltage and I am not even sure that is quite right.  I have to check if this is valid for a sin(w*t) driving force as \n",
    "opposed to cos(w*t)\n",
    "\n",
    "We do this initially by comparing the coefficients of the sin and cos terms but later on we have at doing this\n",
    "using complex analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "54b227ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}, \\  - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}\\right)$"
      ],
      "text/plain": [
       "⎛ A⋅sin(ω⋅t)   -A⋅C⋅R⋅ω⋅cos(ω⋅t) ⎞\n",
       "⎜────────────, ──────────────────⎟\n",
       "⎜ 2  2  2          2  2  2       ⎟\n",
       "⎝C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1   ⎠"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nonTransient.args"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "5b88db11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "     A      \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get sine coefficient\n",
    "sincf = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],nonTransient.args[0].args)))\n",
    "sincf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "620dff99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C R \\omega}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       " -A⋅C⋅R⋅ω   \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get cosine coefficient\n",
    "coscf = reduce(multiplyIt, (filter(lambda x:type(x) not in [cos],nonTransient.args[1].args)))\n",
    "coscf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "dca40fff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A}{\\sqrt{C^{2} R^{2} \\omega^{2} + 1}}$"
      ],
      "text/plain": [
       "        A        \n",
       "─────────────────\n",
       "   ______________\n",
       "  ╱  2  2  2     \n",
       "╲╱  C ⋅R ⋅ω  + 1 "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c3 = sqrt(cancel(sincf**2 + coscf**2))\n",
    "c3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "ebe53008",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import Mul, sympify, re, im\n",
    "import math "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "8475e93c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A C R \\omega e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "                              -t                \n",
       "                              ───               \n",
       "                              C⋅R               \n",
       "  A⋅C⋅R⋅ω⋅cos(ω⋅t)   A⋅C⋅R⋅ω⋅ℯ       A⋅sin(ω⋅t) \n",
       "- ──────────────── + ──────────── + ────────────\n",
       "     2  2  2          2  2  2        2  2  2    \n",
       "    C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1   C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simpeq2 = dsoln.args[1].subs(c1, c1eq.args[0])\n",
    "simpeq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "ee48e2dd",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left\\{ \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} : 1, \\  \\frac{A C R \\omega e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} : 1, \\  \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1} : -1\\right\\}$"
      ],
      "text/plain": [
       "defaultdict(int,\n",
       "            ⎧                          -t                          ⎫\n",
       "⎪                          ───                         ⎪\n",
       "⎪                          C⋅R                         ⎪\n",
       "⎨ A⋅sin(ω⋅t)      A⋅C⋅R⋅ω⋅ℯ        A⋅C⋅R⋅ω⋅cos(ω⋅t)    ⎬\n",
       "⎪────────────: 1, ────────────: 1, ────────────────: -1⎪\n",
       "⎪ 2  2  2          2  2  2            2  2  2          ⎪\n",
       "⎩C ⋅R ⋅ω  + 1     C ⋅R ⋅ω  + 1       C ⋅R ⋅ω  + 1      ⎭)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simpeq2.as_coefficients_dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "d7299630-bec5-4690-962b-554235b9565f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Add' object has no attribute 'all_coeffs'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[42], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43msimpeq2\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mall_coeffs\u001b[49m()\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'Add' object has no attribute 'all_coeffs'"
     ]
    }
   ],
   "source": [
    "simpeq2.coeff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "2488b1d9-7bd9-463c-b8d4-8c9c19107fa6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\sin{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "sin(ω⋅t)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simpeq2.args[0].coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "60485e83-f47c-4fab-8634-3a11d301f1ab",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sin"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(simpeq2.args[0].args[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "03cfa076",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "     A      \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simpeq2.coeff(simpeq2.args[0].args[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "2e9fd9f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "u = symbols('u')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "66f6c8ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A \\sin{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       " A⋅sin(ω⋅t) \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simpeq2.args[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "2baf1a6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "     A      \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get sine coefficient\n",
    "c1 = reduce(multiplyIt, (filter(lambda x:type(x) not in [sin],simpeq2.args[0].args)))\n",
    "c1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "99628c59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFMAAAAhCAYAAAClWJfKAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAGKUlEQVR4nO2ZeYxeUxjGfzMtDVpLLYm1dkrFdKYhYg3RWIOG2qO2aiqWaBElHo8KYhtUpA2iUbFELGmlRUODqqUT04USqpraii7UvnX8cc7VM7ff1+9+naWSzpNM5n7nvOc5733vOe9573NrWlpaWN9g+1Kgl6TbbdcC70g6IPZdApwNDJK0xPaWwInAYcBUSU/aHgyMkHRgylvbubex7mH7cGA0cKHtZuBQ4P3YtwVwC3CGpCUAkpZKGg/0Az6NNAuAP/Pc3ctM2BdoBj6WVFfGpg64Gjgc2Ar4BmgC7pA0M9q8ChwZh/wNLIz9DxW9+faGpNdtzwGGSFpo+3rgldh9CjBN0tfpGNs1QF/gE9vdgAsID6QVSgYTuB+4Bxhpe0NJrZ6C7SHAw8BjwOnAF8DOwFBgGDAzmtYDo4BHgR7ARcA4202SmgtHoArYnkXp+xqYBGknSQvj9VHAA/G6HzCrxNhdCP6/AfQBJkp6JW+02qS2BxG2/x3AdcA+6QS2DyIE8mpJjcnQRcAbtntHu92AzYGXJC2ObeOAG4B9CSsf242ErXaApJU5X5qA6ZKuTNq2B24Djge6Aa8CwyV9C1BuJyXjdwC+jte9gFpJP8buXyid+voBL0s60faOwDzboyR9lRq1Gmh7I+AuYKSkH+Kk/XPEdwPv5gL5HyQti5cNwApgduTeNnKvZFWO2gu4jPBgVq7Oxkfp/LZ3iWO/Ag4BjiCkmLGlfCmDPoSUBCEFTUv6pgBnxUMH25vaPodkxUr6AngROCZPnF+Z1xJWQrYFPwTqkpvZAzgIOLOA0w1AT2BFPDE3IiTtEZLmRZuRwGxJ08pwLAPSE3Ms8IikUYlPo4HnCviT4QNgV9tzge+B67MOSTNs3wNMi3myBWgkBPPZhGMScBLwSEr8XzBt7wxcDuyfm3hA8rs+/m8q4HQ9IR3cCWwK3ArMl3RvnK8WOJWQTjIfGoEFksbEpl6ErYftPsBA4FDblyfzdAN+LeAPAHFLN0TOJuC9XP/D0e8Uj+ZsngCeyHOnK7MR2AL43HbWVgP8ZLtGUguwcWz/uYDf9cDjkuZHx4cBC2yPkzSXkNQ3B+YmYwYDNya/9wfmJdcriIHIYbUypQgkDahsVRzdAWwPJJQ4DbR2bG/gGcKNLyCsVKLt03ky2xtL+jXmtt4kgYplSDNwLnAN4cFBfDC2jwC2y+aPKaWOcNgA/AVsAiyWVORhdjq6294AuA+4W9L7aaftRfGyP2H7zbQ9BRgTD6u3CHmlHrgYMDCd8FBWsmpVZZgKDCIEc1G0Ocv2D4RybBJwgu3ZwIPAHOD5OPYdYDkwwfbNhFW6K3AycFmZA6xTUQtcAWxNuJlWkLQCWExyCBEK27uAqwgn3EzCwfU2q3JpA/CZpN9zlFOBPWzvK+k7Qul1GqFoHkc4kPoTArcUOE7SP9GX5cCxwGaEE3hW9OPL/0MgAWrWx3fzjsJ6927ekegKZjuiK5jtiKw06kqc7YCqD6D4oj8B2IYgq42W9Exnc3QEV1uxNtv8b+BKSfsQXu/utb3JOuDoCK42oc2lUSywT4hqyjrj6AiualFKz6yjgoKe2DYA3fKOV6Owl+NYG7QnV473MMILRQPhlff8+CmjFfJ65hBC4P4gKOh7AufF38Nytr0JSvvQEvNnCvu2wO7AUwSFvZU2WoGjKqwNl+3xtm8qYNqToEtcAfxWziiV4Aop6NG2B/ACcLukGTkHiyrsZTlif2EFvhJXWyFpMjA5zjW+nF26zQsp6FE0HQ+8JmlCCdMiCvsaORIF/uhKCnwBfzoNWZ1ZjYJ+MCEFzLF9cmw7N2qUUExhr8RRjQJfiavTkK3Mwgq6pOmsuaRao8JeiaNaBb6APyn3KEIuz9ADaLE9Mmk7VtKbRfjyyJyoRkGvhHpghqT5UR8dBgy3vV/B8eUU+PTTRKrAV4OxBDkx+5tYoq3IJ5mSyFZmIQW9EllBhb0SqlXgCyPm/ezrKbZ/ApZln1baiu5xkqIKeiUUUdgroVoFvsNhuyehxIOwm3eK9fgySdnXiFa5poiCXgkVFfZKBNUq8J2EAYSSrplwoDpe35wadSnt7YguPbMd0RXMdsS/Ns0EUyXr8zYAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "         -t \n",
       "         ───\n",
       "         C⋅R\n",
       "A⋅C⋅R⋅ω⋅ℯ   \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get cosine coefficient\n",
    "c2 = reduce(multiplyIt, (list(filter(lambda x:type(x) not in [cos],simpeq2.args[1].args))))\n",
    "c2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "36345ddc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "-A⋅C⋅R⋅ω⋅cos(ω⋅t) \n",
       "──────────────────\n",
       "    2  2  2       \n",
       "   C ⋅R ⋅ω  + 1   "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get third coefficient (of exponential term)\n",
    "reduce(multiplyIt, filter(lambda x:type(x) not in [ exp],simpeq2.args[2].args))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "07f2f49c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A^{2} \\left(C^{2} R^{2} \\omega^{2} + e^{\\frac{2 t}{C R}}\\right) e^{- \\frac{2 t}{C R}}}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}}$"
      ],
      "text/plain": [
       "   ⎛            2⋅t⎞  -2⋅t \n",
       "   ⎜            ───⎟  ─────\n",
       " 2 ⎜ 2  2  2    C⋅R⎟   C⋅R \n",
       "A ⋅⎝C ⋅R ⋅ω  + ℯ   ⎠⋅ℯ     \n",
       "───────────────────────────\n",
       "                    2      \n",
       "      ⎛ 2  2  2    ⎞       \n",
       "      ⎝C ⋅R ⋅ω  + 1⎠       "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute c3^2 using pythagoras theorem\n",
    "c3_2 = simplify(c1**2 + c2**2)\n",
    "c3_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "907ce05a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A \\sqrt{C^{2} R^{2} \\omega^{2} + e^{\\frac{2 t}{C R}}} e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "       _________________     \n",
       "      ╱             2⋅t   -t \n",
       "     ╱              ───   ───\n",
       "    ╱    2  2  2    C⋅R   C⋅R\n",
       "A⋅╲╱    C ⋅R ⋅ω  + ℯ    ⋅ℯ   \n",
       "─────────────────────────────\n",
       "         2  2  2             \n",
       "        C ⋅R ⋅ω  + 1         "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find c3 by taking square root\n",
    "c3 = sqrt(c3_2) \n",
    "c3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "56dcb8dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAACMAAAAeCAYAAACmPacqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAADzElEQVR4nO3XW6hWRRQH8N85CqFmpfaQaYl2gzLUYyRCodWDdqMLpSRJEkQhCeGlyIrFyiCQzEgIxYSioB66UYFoiFFmheIlRSEsJDMr1ErU7p4e9hzZfn6mppYPrZfZM3vNWv9Z859Za1ra29sdqWTmAAyMiLdrY6/gsYjYlJkTMAmd0IpZEfFiZk7GFGxHF9wfEYsb7bceMZJKrsXFNSCtOK8AuRd3Y1REDMZVaCmqAzE1IgbhUcxoZrzzkaLIzBHFyI7MHIsrCrBVmdkDT2BQRGyHiNiBF2pgnivfX+K3Zj5ajnKb3seEiNhc+o9gI87A6IgY02ROC3ahD/ZgDt46Htt0bgeQItdgiWrlaw4xpz9OwQcqznRrBoSGbcrMPngS16tIuAQTI+K7zOyLb2q63dEaET9l5p6/WdhALIqIGzPzHGzIzOkRsbVRcb+BzOyPVdiq4sNInIm5RaUfttXmXo2l5XshxmVmr2LrtMy8swZmDUTEFryL0YeLzFwsiIjpNYAz8EbprseAzFyHsRiFl4qT5Zn5NJYWjrRjdg3M6zU/7+AmLGgE09Le3i4z+2Ezfsa+2v9O2BsRvRonZuZKDIuIP5ut8p9IR2QGqRg/tIlO02MYEZcdLxCNYH5HN3wbEbuPt5MjlY5t6oHPsQyPq6I0ADdjUkTsO7SJ4yetEBE/qK7601UnZA2ewtf/FhCO8gY+0XK0N/AJlf/BHEo6Q2b+58SJiJaTisAHFVeZORjTMEKVKLdhJWZGxIrMXKJKkvCHKo3MjIj5xwrmAM6UGnYlflUlwwtxV+nfV9TaMB29cT5exbzMHHKsYPZvU2YOx4eYFhGzGxUzsyd6YBPaImJ1Ge+LLRgfES/X9GfjSlzeeHGWJLssIh6oj9cjMwufNgMCEbFTlUh3YW0x2lt1U+9T1UIdzi5SvRKmHeIG34iDItlxmi7AcNzRDEhNhuJU7Covgy6qrD4lIjbU9KZibUQsbWIDdmJY42BHZNpKu/IwYNrwPAarqsFFmB8Rz3QoFJC34bXa2OzMnFSz011VnDcF07W0hysf2rA8IjZFxCoVqSdm5qU1nf6q18K62tgY7K31B6EeyQPArC/tiGYIMrNrqZF71p2Ul8JqjK+p9yjt7jJ3JM5WirRCicF4s9FP52J0RWYuxJzM7IKPVHVsG+5B4iwVURtX9B5uxYOl/1XRG5eZP+JZVd17Q2auVT3mPmsGpn6ablGdjMmqemYFHsLHKi4NxRcR8UsTMBdk5iVlYd/jYdyOxZinIvQQfIIduK5Z7XxSpYO/AGesbpJnnF5+AAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle \\frac{e^{\\frac{t}{C R}}}{C R \\omega}$"
      ],
      "text/plain": [
       "  t  \n",
       " ─── \n",
       " C⋅R \n",
       "ℯ    \n",
       "─────\n",
       "C⋅R⋅ω"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the phase\n",
    "c1/c2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b24e8dd",
   "metadata": {},
   "source": [
    "The tan function can be equated to the fraction of $ \\frac{\\sin( \\theta )}{\\cos (\\theta )}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "05abad5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\operatorname{atan}{\\left(\\frac{e^{\\frac{t}{C R}}}{C R \\omega} \\right)}$"
      ],
      "text/plain": [
       "    ⎛  t  ⎞\n",
       "    ⎜ ─── ⎟\n",
       "    ⎜ C⋅R ⎟\n",
       "    ⎜ℯ    ⎟\n",
       "atan⎜─────⎟\n",
       "    ⎝C⋅R⋅ω⎠"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(atan(c1/c2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f32d128-ddcd-41a1-a055-e3a5207888f6",
   "metadata": {},
   "source": [
    "### Complex Impedance Analysis "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61093af9",
   "metadata": {},
   "source": [
    "I wish to compare this with the complex analysis of the circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "3bfdd494",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{C R \\omega - i}{C \\omega}$"
      ],
      "text/plain": [
       "C⋅R⋅ω - ⅈ\n",
       "─────────\n",
       "   C⋅ω   "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = R - I / (w*C)\n",
    "zc = cancel(Z)  # express as fraction\n",
    "zc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "f3db2138",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{i}{C R \\omega - i}$"
      ],
      "text/plain": [
       "   -ⅈ    \n",
       "─────────\n",
       "C⋅R⋅ω - ⅈ"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we try and work out Vout as R/Z\n",
    "rzc = (-I/(w*C))/zc\n",
    "rzc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "01ccfae6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{1}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "     1      \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.re(rzc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "b5d08d9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{C R \\omega}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "  -C⋅R⋅ω    \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.im(rzc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "18c46477",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{C^{2} R^{2} \\omega^{2}}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}} + \\frac{1}{\\left(C^{2} R^{2} \\omega^{2} + 1\\right)^{2}}$"
      ],
      "text/plain": [
       "    2  2  2                      \n",
       "   C ⋅R ⋅ω               1       \n",
       "─────────────── + ───────────────\n",
       "              2                 2\n",
       "⎛ 2  2  2    ⎞    ⎛ 2  2  2    ⎞ \n",
       "⎝C ⋅R ⋅ω  + 1⎠    ⎝C ⋅R ⋅ω  + 1⎠ "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.re(rzc)**2 + sympy.im(rzc)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "0436eb4f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{1}{C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "     1      \n",
       "────────────\n",
       " 2  2  2    \n",
       "C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is the square of the magnitude of voltage dividing impedance across R\n",
    "c3_2 = cancel(_)\n",
    "c3_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "225bcd4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH4AAAAUCAYAAABLTIm0AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAGA0lEQVR4nO2ae4xV1RXGfwNqRUnFdy2WV0BoQgiiNdgWxYCg6YvWVzClPNRobUoNtbEmxm8+0Zao4aFRCNEWpFpFkaho1X+k2lpHUUGNWCspSqqtJr5tfTAd/1j7wHHPucPAvXptOl8yWfestffaa5+199pr7TMtHR0d9OD/D72abUAPmoPdmm3A5xW2lwMnAoMlvddse3YFto8A1gFnSbquLGtpZqi3PQj4O7Bc0oymGZLB9teANuB8SfNrtBkGzAImAQOAfsCbwAbgdmCZpH+X2t8PHJ+peQ14Hlgk6dbGzmLbuKuBscAwSe8W/J4dX43LgLeBxbnAdgtwCXABsDvwMHAb8BYwkFgIE4CpwLhS1yOADmBuorsBI4ApwDdsz5G04FOYy6+JRTwb+FXB7HF8BtuHAROB6yT9p6LJb4AZwLPA6ZI2ZP37AHOAoSXeEGA/4K+SlLU/h1hgPwMa7nhJj9p+Djjb9jxJ/4UGO972DOA7wOHAIcBHwNPAYkm/y9q2AsVLmG57ekk8U9KyndGXdA4iHR1AKzCPcGJf4BmgVdKaHUxjFtAC3FKhfw7h9I3AWEnv5G3SYrksLYACRyb6eMV49yZ6UJUxts8GlgDzJf28ltG2NwFDgC9J+lcmvpl4H8cD90Hjs/rFRLh7EFiYBhwIrLA9N2u7FliUfm8AXPpbvwv6yhgIPAoMAlYQThwJ3GH7uB3MYSLQDjxSZto+hDgCtgKnVjm9jCxadOX4IjJszAW2DwYuB/7J9k1SC4Xur1fI/pzothyj0aF+pKRNZYbtPYA/AL+0vUTSPwAkrbW9mQhx6yW11qMvw3hid7vU7yZid/0CeKDKeNt7A6OBjRWZ/HnAnkTS9kxV/y5QOH5dNt4BwJXpcV5Fv4uBLwIXlROzGtic6IgK2WOJHlMwGrrjcycl3ofANcQim/AZ6XsRuDTrdx/wEnBUF0P2B3oDr1TIpiR6Q5dGZ0jJ4Jj0+F3brbbn2r4BeIEIz+fmWX1aFGcQSeb13RiqWKj75gJJbwHvE9UHkO34tAMHdmdCCTdK+mGp/wAi252QBumTte+/E7rr0bdeUnsFfwtwdBdD7p/oG5kdfYHDiGy8bQdm5xgG7JN+52f0e8DJku6lM04FvgCszMrCo4jk8SpJD5fa75XoBzXseB04uHjIQ/0mYmV0Fy+XDBpCnKv7Ag8B9xMlTjtx1k5PE+kW6tT3Zg3+VrqOcsW5vGfGPzDRt8tO6CaKMP9bSbMAbO9H2D8f+L3twZJym8cn+seM/23gNOCKjF/kCn+rYUcfts/vk46XtFOhOMMcYsfMlLSsLLA9lZhoM/V1B68mun/GL8JoH9u9a0STWuh0vkt6HVhg+2jgFGAacHXWb3iiz2X8yYm+VDBs9wK+mR7zhVLI+xEVD9DYM75YcasqZMfW6FO8wN4N0lcvXiFu04aXmZJeJfKGPdi+EyuRXnIZXWX0xTXq1ApZcTxsS+psf5XtOUo5pE8kysE2SS9W6BpOlKjrC0YjHb850fFlpu3JwJk1+rxBnJsDKmS7oq8uSOogSscDbA/NxMXlyrW2O2XOtltsn0iUnAWvF3EHsZUoWXM8QBxLY21/OZO9luioQj9R2j2R+MMTf6/Eh7ilq8LY0nhAY8u5a4GZwK22byPO/5HACcBK4lz6BCS9a7sNGGf7RuLeuh24c1f0NQirgJOIkPpCiX8V4YRZwNPp7v154lLpK0SoPRS4qdRnBHF5tEFSp9xJ0ke27wFOB75PVCsFVhPRYqHt0cQCOpKoxdcCy23fBXyPWARLJd1RY06TiPe6Td6wHS/pKeA44u76W8CPiRr0B8TNUy1MA+4mHCriLntMHfrqxSrirP9RmSmpQ9IZyZY1RL3/EyL6jAL+QtzqzS516yrMF1id6EkZ/wri0qodOIfYpJMktaXnvYk7kA+BcxOvE2zvQ5SiayRtKfhN/Tr3eYXtC4kPGmMkPdlse+qB7Z8S0WqcpD8V/J5/xKjGAiJrvqTZhtSD9L3gQmBV2enQ4/hKpPN4GrAuXeP+r2IQsBQ4Pxd8DFJEJqq+3vTWAAAAAElFTkSuQmCC",
      "text/latex": [
       "$\\displaystyle - \\operatorname{atan}{\\left(C R \\omega \\right)}$"
      ],
      "text/plain": [
       "-atan(C⋅R⋅ω)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phase = atan(sympy.im(rzc)/sympy.re(rzc))\n",
    "phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "26cdf8e7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{1}{\\sqrt{\\omega^{2} + 1}}$"
      ],
      "text/plain": [
       "     1     \n",
       "───────────\n",
       "   ________\n",
       "  ╱  2     \n",
       "╲╱  ω  + 1 "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = sqrt(c3_2).subs([(A,1), (C,1), (R,1)])\n",
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "75116894",
   "metadata": {},
   "outputs": [],
   "source": [
    "f1 = lambdify(w, u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "25585a9d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1300x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
    "fig.set_figwidth(13)\n",
    "\n",
    "f1 = lambdify(w, u)\n",
    "t1 = np.linspace(0, 4, 8000)\n",
    "y = f1(t1)\n",
    "y2 = 1 - y\n",
    "\n",
    "ax1.title.set_text(\"frequency vs phase $V_c$\")\n",
    "ax1.set_xlabel(\"Frequency ($ \\omega $)\")\n",
    "ax1.set_ylabel(\"cos(Phase)\")\n",
    "ax1.plot(t1, y)\n",
    "ax1.grid()\n",
    "\n",
    "\n",
    "ax2.title.set_text(\"frequency vs phase $V_R$\")\n",
    "ax2.set_xlabel(\"Frequency ($ \\omega $)\")\n",
    "ax2.set_ylabel(\"cos(phase)\")\n",
    "ax2.plot(t1, y2)\n",
    "ax2.grid()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "0b7c1ec1-c6d8-448f-9bc8-970f3c457ebe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\omega$"
      ],
      "text/plain": [
       "ω"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = getSym(simpeq2, \"omega\")\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "f30ac994",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\pi e^{- t}}{1 + 4 \\pi^{2}}$"
      ],
      "text/plain": [
       "     -t \n",
       "2⋅π⋅ℯ   \n",
       "────────\n",
       "       2\n",
       "1 + 4⋅π "
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expdropoff = simpeq2.args[1].subs([(C*R, 1), (A,1), (f,1), (w, 2*pi)])\n",
    "expdropoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "cc21b169",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{\\sin{\\left(2 \\pi t \\right)}}{1 + 4 \\pi^{2}} - \\frac{2 \\pi \\cos{\\left(2 \\pi t \\right)}}{1 + 4 \\pi^{2}} + \\frac{2 \\pi e^{- t}}{1 + 4 \\pi^{2}}$"
      ],
      "text/plain": [
       "                                   -t \n",
       "sin(2⋅π⋅t)   2⋅π⋅cos(2⋅π⋅t)   2⋅π⋅ℯ   \n",
       "────────── - ────────────── + ────────\n",
       "        2              2             2\n",
       " 1 + 4⋅π        1 + 4⋅π       1 + 4⋅π "
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fn = simpeq2.subs([(C*R, 1), (A,1), (f,1), (w, 2*pi)])\n",
    "fn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "d89afff6-a5d4-4917-a29e-0021b7bc6b59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 184,  588,  989, 1389, 1789, 2189, 2589, 2989, 3389, 3789])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1 = lambdify(t, fn)\n",
    "f3 = lambdify(t, expdropoff)\n",
    "t1 = np.linspace(0, 10, 4000)\n",
    "y2 = np.sin(2*np.pi*t1)\n",
    "y = f1(t1)\n",
    "pks = find_peaks(y)[0]\n",
    "pks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "fdb9e294-92b9-4159-a301-be102ee9c31d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ \\left( 0.460115028757189, \\  0.254479337914674\\right), \\  \\left( 1.47036759189797, \\  0.192790174277999\\right), \\  \\left( 2.47311827956989, \\  0.170255738060344\\right), \\  \\left( 3.47336834208552, \\  0.161983472100571\\right), \\  \\left( 4.47361840460115, \\  0.15894225432955\\right), \\  \\left( 5.47386846711678, \\  0.157824705183785\\right), \\  \\left( 6.47411852963241, \\  0.157414411932577\\right), \\  \\left( 7.47436859214804, \\  0.157263993225821\\right), \\  \\left( 8.47461865466367, \\  0.157208907812005\\right), \\  \\left( 9.47486871717929, \\  0.157188639481615\\right)\\right]$"
      ],
      "text/plain": [
       "[(0.4601150287571893, 0.25447933791467403), (1.4703675918979744, 0.19279017427 ↪\n",
       "\n",
       "↪ 799905), (2.4731182795698925, 0.17025573806034372), (3.4733683420855215, 0.1 ↪\n",
       "\n",
       "↪ 6198347210057146), (4.47361840460115, 0.15894225432954986), (5.4738684671167 ↪\n",
       "\n",
       "↪ 79, 0.1578247051837846), (6.474118529632408, 0.15741441193257652), (7.474368 ↪\n",
       "\n",
       "↪ 5921480365, 0.15726399322582088), (8.474618654663665, 0.15720890781200475),  ↪\n",
       "\n",
       "↪ (9.474868717179294, 0.15718863948161516)]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[(t1[ii],y[ii]) for ii in pks]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "054c609f-9af7-41ce-afbd-96518bff30bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1200x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax3) = plt.subplots(1,2)\n",
    "fig.set_figwidth(12)\n",
    "\n",
    "f1 = lambdify(t, fn)\n",
    "f3 = lambdify(t, expdropoff.subs(w, 2*pi))\n",
    "t1 = np.linspace(0, 10, 4000)\n",
    "y2 = np.sin(2*np.pi*t1)\n",
    "y = f1(t1)\n",
    "\n",
    "ax1.title.set_text(\"Amplitude vs time from $ V_C $ formula\")\n",
    "ax1.set_xlabel(\"Time (RC units)\")\n",
    "ax1.set_ylabel(\"Relative Amplitude\")\n",
    "ax1.plot(t1, y)\n",
    "ax1.grid()\n",
    "\n",
    "\n",
    "t1 = np.linspace(0, 10, 4000)\n",
    "y = f3(t1)\n",
    "\n",
    "ax3.title.set_text(\"Exponential drop off component\")\n",
    "ax3.set_xlabel(\"Time (RC units)\")\n",
    "ax3.set_ylabel(\"Relative Amplitude\")\n",
    "ax3.plot(t1, y)\n",
    "ax3.grid()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "fbf1e1a0-5d37-42f5-8f84-5a0e7231ba11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([], dtype=int64), {})"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_peaks(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdae93cf-493c-4aef-89cd-3844b6285fb5",
   "metadata": {},
   "source": [
    "## Two RC Filter Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "c42e81ff",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://images.kiwiheretic.xyz/RC-filter1.jpg\" width=\"400\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "Image(url='https://images.kiwiheretic.xyz/RC-filter1.jpg', width=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3e5d823",
   "metadata": {},
   "source": [
    "I am assuming that the voltage in the direction of conventional current produces a positive voltage above ground.\n",
    "That means $ R_1 ( i_2 - i_1) $ is considered to be a positive voltage above ground because the current is flowing to ground.  However the same must be true of $ R_2 i_2 $ if we look at $ R_1 ( i_2 - i_1) $ being the voltage source of the last stage.\n",
    "\n",
    "There are two equations:\n",
    "\n",
    "$$ V_{in} = V_{C1} + R_1 (i_1 - i_2) $$\n",
    "$$ R_1 ( i_2 - i_1) = V_{C2} + R_2 i_2 $$\n",
    "\n",
    "These can be rearranged so that all the i's are on the right and everything else on the left.\n",
    "\n",
    "$$ V_{in} - V_{C1} = R_1 i_1 - R_1 i_2) $$\n",
    "$$  V_{C2} = R_1 ( i_2 - i_1) -  R_2 i_2 = (R_1 - R_2) i_2 - R_1 i_1 $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c914fb13",
   "metadata": {},
   "source": [
    "In matrix form this looks like:\n",
    "\n",
    "$$ \\begin{pmatrix}\n",
    "V_{in} - V_{C1} \\\\ V_{C2}\n",
    "\\end{pmatrix} \n",
    "=\n",
    "\\begin{pmatrix}\n",
    "R_1 & -R_1  \\\\\n",
    "-R_1 & R_1 - R_2 \\\\\n",
    "\\end{pmatrix}\n",
    "\\begin{pmatrix}\n",
    "i_1 \\\\ i_2\n",
    "\\end{pmatrix} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "e91de147",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(R_1, R_2, V_{in}, Vc1, Vc2, C_1, C_2)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_0, A_1, A_2, B_1, B_2, R1, R2, R3, Vin, C1, C2 = symbols(\"A_0 A_1 A_2 B_1 B_2 R_1 R_2 R_3 V_{in} C_1 C_2\")\n",
    "Vc1 = Function('Vc1')\n",
    "Vc2 = Function('Vc2')\n",
    "Vc3 = Function('Vc3')\n",
    "R1,R2, Vin, Vc1, Vc2, C1,C2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "14c67acf",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}R_{1} & - R_{1}\\\\- R_{1} & R_{1} - R_{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡R₁     -R₁  ⎤\n",
       "⎢            ⎥\n",
       "⎣-R₁  R₁ - R₂⎦"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = Matrix([[R1, -R1], [-R1, R1-R2]]); m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "34ec4cdb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\\\operatorname{Vc}_{2}{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡V_{in} - Vc₁(t)⎤\n",
       "⎢               ⎥\n",
       "⎣    Vc₂(t)     ⎦"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Matrix([Vin-Vc1(t), Vc2(t)]);v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "a6128b46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- R_{1} + R_{2}}{R_{1} R_{2}} & - \\frac{1}{R_{2}}\\\\- \\frac{1}{R_{2}} & - \\frac{1}{R_{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-R₁ + R₂  -1 ⎤\n",
       "⎢────────  ───⎥\n",
       "⎢ R₁⋅R₂    R₂ ⎥\n",
       "⎢             ⎥\n",
       "⎢  -1      -1 ⎥\n",
       "⎢  ───     ───⎥\n",
       "⎣  R₂      R₂ ⎦"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "eb0fd76f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R_{2}} + \\frac{\\left(- R_{1} + R_{2}\\right) \\left(V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\right)}{R_{1} R_{2}}\\\\- \\frac{V_{in} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R_{2}} - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R_{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  Vc₂(t)   (-R₁ + R₂)⋅(V_{in} - Vc₁(t))⎤\n",
       "⎢- ────── + ────────────────────────────⎥\n",
       "⎢    R₂                R₁⋅R₂            ⎥\n",
       "⎢                                       ⎥\n",
       "⎢        V_{in} - Vc₁(t)   Vc₂(t)       ⎥\n",
       "⎢      - ─────────────── - ──────       ⎥\n",
       "⎣              R₂            R₂         ⎦"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mtmp = m.inv()*v\n",
    "mtmp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "7f06d9c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -Vc₂(t) \n",
       "──(Vc₁(t)) = ────────\n",
       "dt             C⋅R   "
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn_1 = Eq(C1 * Vc1(t).diff()/C, mtmp[0]/C)\n",
    "eqn1 = eqn_1.subs([(R1, R), (R2, R), (C1,C)])\n",
    "eqn1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "1fdca3e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "d         \n",
       "──(Vc₂(t))\n",
       "dt        "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vc2(t).diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "8e3d540c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = \\frac{- V_{in} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -V_{in} + Vc₁(t) - Vc₂(t)\n",
       "──(Vc₂(t)) = ─────────────────────────\n",
       "dt                      C⋅R           "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn_2 = Eq(Vc2(t).diff(), simplify(mtmp[1]/C))\n",
    "eqn2 = eqn_2.subs([(R1, R), (R2, R)])\n",
    "eqn2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "8ae391f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -Vc₂(t) \n",
       "──(Vc₁(t)) = ────────\n",
       "dt             C⋅R   "
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "03271341",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.mul.Mul"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(eqn2.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "c7d7558d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.add.Add"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(expand(eqn2.rhs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "68e3840e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isinstance(eqn1, sympy.Equality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "13085f87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.function.Derivative"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(eqn1.lhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "428b07d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isinstance(eqn1.lhs.args[0], sympy.Function)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "15a87aec",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fn1(t, y, R, C, f):\n",
    "    \"\"\" y is an array of size 2\"\"\"\n",
    "    #print (t,y,R,C,f)\n",
    "    yp1 = (-y[1]) / (C*R)\n",
    "    yp2 = (y[0] - y[1] - math.sin(2 * math.pi * f * t))/(C*R)\n",
    "    return [ yp1, yp2 ]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "93d7f0da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ 0.0, \\  -0.0628318489376257\\right]$"
      ],
      "text/plain": [
       "[0.0, -0.06283184893762572]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fn1(0.0001, [0,0], 1000, 0.00001, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "8217b134",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1400x1000 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(2,3)\n",
    "fig.set_figwidth(14)\n",
    "fig.set_figheight(10)\n",
    "\n",
    "farr = [1,5]\n",
    "\n",
    "start_idx = 8\n",
    "for ax1, ax2, ax3 in axs:\n",
    "    freq = farr.pop(0)\n",
    "    res = solve_ivp(fn1, [0,5], [0,0], 'RK45', args = (1000,0.00001,freq), first_step=0.0001)\n",
    "    ax1.title.set_text(\"$V_{{C1}} $ freq = {} Hz\".format(freq))\n",
    "    ax1.set_ylabel(\"$V_{C1}$\")\n",
    "    ax1.set_xlabel(\"Time\")\n",
    "    ax1.plot(res.t[start_idx:]/(math.pi*2), res.y[0][start_idx:])\n",
    "    ax1.grid()\n",
    "\n",
    "    ax2.title.set_text(\"$V_{{C2}} $ freq = {} Hz\".format(freq))\n",
    "    ax2.set_ylabel(\"$V_{C2}$\")\n",
    "    ax2.set_xlabel(\"Time\")\n",
    "    ax2.plot(res.t[start_idx:]/(math.pi*2), res.y[1][start_idx:])\n",
    "    ax2.grid()\n",
    "    \n",
    "    vr1 = np.sin(2 * math.pi * freq * res.t) - res.y[0] - res.y[1]\n",
    "    ax3.title.set_text(\"$V_{{out}} $ freq = {} Hz\".format(freq))\n",
    "    ax3.set_ylabel(\"$V_{out}$\")\n",
    "    ax3.set_xlabel(\"Time\")\n",
    "    ax3.plot(res.t[start_idx:]/(math.pi*2), vr1[start_idx:])\n",
    "    ax3.grid()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "1db9ef88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAAcCAYAAADhhWo2AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAJOElEQVR4nO2ce7BVVR3HPxepRC0dtVREJRVfU3oFRQxxlHxmKahZWpKITIpSJDTJqPP1q6M5+SBLsREnoVKLBLXEV75yKl+kmAJlmGYmCYmAQCjo7Y+19mWz7z7n7AP3HHnsz8yZdc5av73Xb5/fWWv91m+tdVra2tooiu2zgdGSehW+qKSkJJcudcq3AjM6X42Sko2PNWl8zzVAj5KSjY6ulQpstwLjgH7AHGAY8Fng0qZoVlKygZPb+Gz3An4P3AgMB/YEJgObsR67nbYnAccCn5a0tOA1fYDpwHBJNzdSv5J8NlS7teQFXGw/ALwl6bRU3gTgeEnb5cjfCpwGnCtpfLUKbT8IHAmcKOnOtdS/MLYPBJ4Cxki6Nqf8O8C1wNck3ZYpu5PgAfSStKQZ+jaD0m7tctsBbwDjJY3MlPUCzgSOAnYGtgIWAs8DU4GJkpal5JPvKc184CXgOkm/TjI7zPls7xQrGpcpWkHlUW9CTM+qUJ7cuydwBDAX+G012QZwObCYMJrn0Semf84p+z6wPfCtBuj1YVLaLXACoS1MTTJst9i+DJgJXAAsB+4ArgEeAvYHbgAeyNGnjTA9c9T/cUInMDl2FkB+wGV/4H1Cy07TmwqNT9JjhJa9v+3eVR5yGNAC3CJpZRW5TsX2HoQfz2RJ/6sg1gdYQniO1ZD0NPBX4Ju26w1SrbOUdmtnMPAWoZEk/BS4CPg70Cqpv6RzJF0g6VSgRyyfk9J3V2Br4CUFLpF0kaSTgfOi2LcT+bw5XxuwCfAx4L140wHAQcAPqzzABOAqwhzxnGyh7U2AofH+HXxw232B0cAhwLbAAuAF4GZJk6vUW4QzCT+eX+XUeyXwvVTWB7aT90Mk/Ty+/yVwCcGlyPZ26zMbtd1sfwIYCNwm6f2Ydz5wBjAb6Cfpnex1sTO43Ha3VPYBMc0bhe+P6aeSjLzeYDrwLnC17d1sHwf8IpbNyJFPmERorKfa3iyn/FhgR+AhSa+kC2wPB/4EDIrpNcC0qOiIKnUW5QjCaP5kTtmzUXdi3U69HkvJ/TGmWX9+fWdjt9sXgY8CdwLY3oHgKq4ETslreGkyI3K1xrd7TGcnGR1GPklzbQ8FrgSGENb1JgJjyBnaU9fNt30XcEp8TcyIDI/pTelM2/sA4wl+/QBJMzPlPSrVWQTbmxPWJ2fnRcokTba9FfANYJKkm7IykWdiemiN+kYRJuVFmSHprjrkO5XSbgwGlgIPxs+jgE0JgZQX61Q7aXzT05m2twWujh+vTPJzlxok3Q7cns0uUPlNBAOeRcqIsTf5AjAPuDtzzTlRj8uyBoy6vF6g3mrsSHCj51aRSeY7z1YSkLTI9nJCxKsao4Bd6tBvEnBXHfKNYKO0m+1NgWOA+yQtj9mDYvqzepS13ZLS53jbAwn67wIcT/AyR6SjnRUX2deQR4CXgf6295aUDLFDY10TJa3IXNMvpvfVurntQwkjcB+gOzBU0sQal20T07eryPQmRHNfqHGvBUCHpZY0knrWuMdaY/tV6mvgt0r6epXyRtttLHAiYb34XYIbObbGyNIMux0JbMEql3MLYA/C/PapGvfM0gvYMr4fnSlbCpws6f50ZqdG7iSlJ+VnQXuPMIzwQBNyLtsqpv8uUMUWwIuEiFGl6FeWRG7TvELbXQk7d2ZJerfGvbrVUW8jeRn4Wx2vN6rdrAl2O4zgon6OENxYCTxke+sq1zTDbicS5rvT4udPxnRxeu2uIInLeYukFkkthA7kfGBz4PboJrfTNT5I8aMNOcSKEm4hrHEMiT3eAGBX4BFJc3IuXxjTHQlh4Wr13AvcG3WeWFC9eTHdpkL5PgQDV3RdYn1dCD+4V2rIjaLBcz5Jn69HviCNtNvR6c+2TwcWAf2pvG7YULvFKO6XCM+3KGYnc8tutjdJop8F6TDfk7QAGGf7YODLwOnAj5PyrlEo3XjWCklv2v4NcBLBfx4ciypNiJ+Mih9LDSOuIXMJOwz2rFDeGtNaG8b3JIS9Z9SQG8X6N+drtt0+TvC6qrmUjbbboYSG3b5bR9I82/8k2O8w4OFKN7XdRdIHqaxqkc6bCY3vVLKNrxpreIZvAsGIo4H9gP+SesgMNwJnAxfbfkDSrEz9PdZm8i6pzfbjwEm2d8/pxZOedXGNWyVznEdr1Nezfi3XGZplt+sIjeGJSoo0wW6DgQ/oGEgaR1jPHm/7BEmrdSzRHT+GMB8+JeZ1IWxOWUnHzSlJ3QuBfra7S3oDigVcWom9hu2rgH2zbkQODwKvAn3j5+slvZcnKGmW7RHAT4DnbN9N2FWwDXAg4cs9vICe1ZhC+FEdTWpHQiTpqS63/RmC6zEzHZWKHEVYc8oaa0Oi4XazfS1hQf6QAm5dQ+wWG9Ag4AlJb2bkfwTsS1jgfyHu1XyJENjZKereA0jvI92LEI94PhU1bUfSCtv3EvbRDiZsSysUcGll1dDeF3i61gWZCTzkT9jT8hMID3UPYbj/LiE8Oz9RdC2ZQphDDMmp+3FgJMF4IwlLKq1pGdtbEox1j6R/dYI+6ySNtpvtcQTXa6CkfxRQqVF2O4DQkKaSQVKbpGHAcfG5WoFzCYGofQmj9Rmsvl+0msuZkHgQJyUZq51qcP4ZvkcJX9gdwEdSN5staZ8qlTUU20uA8wosNSTyY4ErgN6S6joQbHskoUccIOkP9epaAravA74CHJ5ayihyXafbzfYVwFhg1+yunWbS7na6+hm+6cDBMT0IeI2wXtNU4jpMsk2nC7Bz7DAWSHqtxuXjCHOUSwlRrqJ1diMYakrZ8NYM2zcQIn2DgLdtbx+Llqj2Ea1G2G0wwUX80BoerO52Xg9Mi7u250iaBvwOmBcniDsA7wDPSPqPpGqRqkZxAMEFfo6wduP4vubp+uiLnw5Mj1uXitKTEPEbU6+yJe2MIEQ4HyZEMZNXze+0EXaTtLek1jru1RBa2trakjN8rwF9JSV74bA9HthN0tG2LwaOkjTgw1K2pGRDIhn5ipzha6X886SSkk4jaXzpM3zAamf4kga3H/CXpmpXUrIBkwRc0mf4fkBYt0j+02NGSnYv292BZZIWNlHPkpINji4QzvARVuyPIWxcvpBwtGQZq87wXQh8FXid8N8YJSUla0Huv5eVlJQ0nv8DJ6pQbsVeXfQAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -Vc₂(t) \n",
       "──(Vc₁(t)) = ────────\n",
       "dt             C⋅R   "
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "d8c3b4e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = \\frac{- V_{in} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -V_{in} + Vc₁(t) - Vc₂(t)\n",
       "──(Vc₂(t)) = ─────────────────────────\n",
       "dt                      C⋅R           "
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "184ca226",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(a_2*omega, -a_1*omega), (a_3/(C*R), a_4/(C*R))]\n",
      "[(a_4*omega, -a_3*omega), (-a_1/(C*R), -a_2/(C*R)), (a_5/(C*R), a_6/(C*R)), (a_3/(C*R), a_4/(C*R))]\n",
      "[a_1, a_2, a_3, a_4, a_5, a_6]\n"
     ]
    }
   ],
   "source": [
    "sysEqns = systemEqns()\n",
    "\n",
    "res1 = sysEqns.extractCoeffsFromDiffEqn(eqn1)\n",
    "print (res1)\n",
    "res2 = sysEqns.extractCoeffsFromDiffEqn(eqn2)\n",
    "print (res2)\n",
    "print (sysEqns.symbols_used)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "71203e92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & - \\omega & \\frac{1}{C R} & 0 & \\frac{1}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & \\omega & \\frac{1}{C R} & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                1           ⎤\n",
       "⎢-ω    0    0   ───   0    0 ⎥\n",
       "⎢               C⋅R          ⎥\n",
       "⎢                            ⎥\n",
       "⎢           1                ⎥\n",
       "⎢ 0    ω   ───   0    0    0 ⎥\n",
       "⎢          C⋅R               ⎥\n",
       "⎢                            ⎥\n",
       "⎢     -1         1         1 ⎥\n",
       "⎢ 0   ───  -ω   ───   0   ───⎥\n",
       "⎢     C⋅R       C⋅R       C⋅R⎥\n",
       "⎢                            ⎥\n",
       "⎢-1         1         1      ⎥\n",
       "⎢───   0   ───   ω   ───   0 ⎥\n",
       "⎣C⋅R       C⋅R       C⋅R     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M, syms_used = sysEqns.orderedMatrix([res1, res2])\n",
    "display(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "eed5dd94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ a_{1}, \\  a_{2}, \\  a_{3}, \\  a_{4}, \\  a_{5}, \\  a_{6}\\right]$"
      ],
      "text/plain": [
       "[a₁, a₂, a₃, a₄, a₅, a₆]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "syms_used"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbb4a6e8",
   "metadata": {},
   "source": [
    "The rows of M1 are in order of a1, a2, a3, a4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "9c052a4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\omega & 0 & 0 & \\frac{1}{C R}\\\\0 & \\omega & \\frac{1}{C R} & 0\\\\0 & - \\frac{1}{C R} & - \\omega & \\frac{1}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & \\omega\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                1 ⎤\n",
       "⎢-ω    0    0   ───⎥\n",
       "⎢               C⋅R⎥\n",
       "⎢                  ⎥\n",
       "⎢           1      ⎥\n",
       "⎢ 0    ω   ───   0 ⎥\n",
       "⎢          C⋅R     ⎥\n",
       "⎢                  ⎥\n",
       "⎢     -1         1 ⎥\n",
       "⎢ 0   ───  -ω   ───⎥\n",
       "⎢     C⋅R       C⋅R⎥\n",
       "⎢                  ⎥\n",
       "⎢-1         1      ⎥\n",
       "⎢───   0   ───   ω ⎥\n",
       "⎣C⋅R       C⋅R     ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M1 = M[:4,:4]\n",
    "display(M1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "798afa00",
   "metadata": {},
   "outputs": [],
   "source": [
    "A,B,D,E,F,G,H,  w = symbols('A B D E F G H \\omega')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "82281ff1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\- \\frac{A}{C R}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ 0 ⎤\n",
       "⎢   ⎥\n",
       "⎢ 0 ⎥\n",
       "⎢   ⎥\n",
       "⎢ 0 ⎥\n",
       "⎢   ⎥\n",
       "⎢-A ⎥\n",
       "⎢───⎥\n",
       "⎣C⋅R⎦"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "amat = Matrix([0,0, 0,-A/(C*R)])\n",
    "amat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "1be85e38",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{A \\left(C^{3} R^{3} \\omega^{2} - C R\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}\\\\\\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A \\left(C^{4} R^{4} \\omega^{3} - C^{2} R^{2} \\omega\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡       ⎛ 3  3  2      ⎞      ⎤\n",
       "⎢    -A⋅⎝C ⋅R ⋅ω  - C⋅R⎠      ⎥\n",
       "⎢─────────────────────────────⎥\n",
       "⎢    ⎛ 4  4  4    2  2  2    ⎞⎥\n",
       "⎢C⋅R⋅⎝C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1⎠⎥\n",
       "⎢                             ⎥\n",
       "⎢           A⋅C⋅R⋅ω           ⎥\n",
       "⎢   ───────────────────────   ⎥\n",
       "⎢    4  4  4    2  2  2       ⎥\n",
       "⎢   C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1   ⎥\n",
       "⎢                             ⎥\n",
       "⎢            2  2  2          ⎥\n",
       "⎢        -A⋅C ⋅R ⋅ω           ⎥\n",
       "⎢   ───────────────────────   ⎥\n",
       "⎢    4  4  4    2  2  2       ⎥\n",
       "⎢   C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1   ⎥\n",
       "⎢                             ⎥\n",
       "⎢     ⎛ 4  4  3    2  2  ⎞    ⎥\n",
       "⎢  -A⋅⎝C ⋅R ⋅ω  - C ⋅R ⋅ω⎠    ⎥\n",
       "⎢─────────────────────────────⎥\n",
       "⎢    ⎛ 4  4  4    2  2  2    ⎞⎥\n",
       "⎣C⋅R⋅⎝C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1⎠⎦"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeffs = M1**-1 * amat\n",
    "coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "08cf3dfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "d,b,f,e = coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "c2603919",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega \\left(\\omega - \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       " A⋅C⋅R⋅ω⋅(\\omega - ω)  \n",
       "───────────────────────\n",
       " 4  4  4    2  2  2    \n",
       "C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Do a sanity check - should equal zero\n",
    "simplify(b*w+f/(C*R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "60c8e5ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A \\left(\\omega - \\omega\\right) \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "               ⎛ 2  2  2    ⎞\n",
       "A⋅(\\omega - ω)⋅⎝C ⋅R ⋅ω  - 1⎠\n",
       "─────────────────────────────\n",
       "    4  4  4    2  2  2       \n",
       "   C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1   "
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(e/(C*R)-d*w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "6f02f484",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A \\left(- C^{4} R^{4} \\omega \\omega^{3} + C^{2} R^{2} \\omega \\omega - 1\\right)}{C R \\left(C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1\\right)}$"
      ],
      "text/plain": [
       "  ⎛   4  4         3    2  2             ⎞\n",
       "A⋅⎝- C ⋅R ⋅\\omega⋅ω  + C ⋅R ⋅\\omega⋅ω - 1⎠\n",
       "──────────────────────────────────────────\n",
       "          ⎛ 4  4  4    2  2  2    ⎞       \n",
       "      C⋅R⋅⎝C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1⎠       "
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This reduces to -A/(C*R) but simplify doesn't do much of a job of reducing it.  If you look carefully you can see why.\n",
    "simplify(e*w-(d-f)/(C*R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "69e5d7b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\left(\\omega - \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "   2  2  2             \n",
       "A⋅C ⋅R ⋅ω ⋅(\\omega - ω)\n",
       "───────────────────────\n",
       " 4  4  4    2  2  2    \n",
       "C ⋅R ⋅ω  - C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify((e-b)/(C*R)-f*w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "919c4009",
   "metadata": {},
   "source": [
    "This is a little bit at variance with the results downstairs but not by much.  It indicates that I may have a sign issue somewhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "bcaecaa0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vc2 = E*sin(w*t)+F*cos(w*t)\n",
    "vc2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "58abd6f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "B⋅sin(\\omega⋅t) + D⋅cos(\\omega⋅t)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vc1 = B*sin(w*t)+D*cos(w*t)\n",
    "vc1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "eabd944b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{\\partial}{\\partial t} \\left(B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)}\\right) = - \\frac{E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}}{C R}$"
      ],
      "text/plain": [
       "∂                                       -(E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)) \n",
       "──(B⋅sin(\\omega⋅t) + D⋅cos(\\omega⋅t)) = ─────────────────────────────────────\n",
       "∂t                                                       C⋅R                 "
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1 = eqn1.subs([(Vc1(t), vc1), (Vc2(t), vc2)])\n",
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "ee42ac89",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{\\partial}{\\partial t} \\left(E \\sin{\\left(\\omega t \\right)} + F \\cos{\\left(\\omega t \\right)}\\right) = \\frac{- A \\sin{\\left(\\omega t \\right)} + B \\sin{\\left(\\omega t \\right)} + D \\cos{\\left(\\omega t \\right)} - E \\sin{\\left(\\omega t \\right)} - F \\cos{\\left(\\omega t \\right)}}{C R}$"
      ],
      "text/plain": [
       "∂                                       -A⋅sin(\\omega⋅t) + B⋅sin(\\omega⋅t) + D ↪\n",
       "──(E⋅sin(\\omega⋅t) + F⋅cos(\\omega⋅t)) = ────────────────────────────────────── ↪\n",
       "∂t                                                                             ↪\n",
       "\n",
       "↪ ⋅cos(\\omega⋅t) - E⋅sin(\\omega⋅t) - F⋅cos(\\omega⋅t)\n",
       "↪ ──────────────────────────────────────────────────\n",
       "↪     C⋅R                                           "
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2 = eqn2.subs([(Vc1(t), vc1), (Vc2(t), vc2), (Vin, A*sin(w*t))])\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "22a2f62d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle B \\omega \\cos{\\left(\\omega t \\right)} - D \\omega \\sin{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "B⋅\\omega⋅cos(\\omega⋅t) - D⋅\\omega⋅sin(\\omega⋅t)"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1.lhs.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "8781faf8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle E \\omega \\cos{\\left(\\omega t \\right)} - F \\omega \\sin{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "E⋅\\omega⋅cos(\\omega⋅t) - F⋅\\omega⋅sin(\\omega⋅t)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2.lhs.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "86a4b00e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( B \\sin{\\left(\\omega t \\right)}, \\  D \\cos{\\left(\\omega t \\right)}, \\  - A \\sin{\\left(\\omega t \\right)}, \\  - E \\sin{\\left(\\omega t \\right)}, \\  - F \\cos{\\left(\\omega t \\right)}\\right)$"
      ],
      "text/plain": [
       "(B⋅sin(\\omega⋅t), D⋅cos(\\omega⋅t), -A⋅sin(\\omega⋅t), -E⋅sin(\\omega⋅t), -F⋅cos( ↪\n",
       "\n",
       "↪ \\omega⋅t))"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2.rhs.args[2].args"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3e1066b",
   "metadata": {},
   "source": [
    "Afte cancelling for sines and cosines we end up with the following equations:\n",
    "\n",
    "$$ F + B \\omega C R = 0 $$\n",
    "$$ E - D \\omega C R = 0 $$\n",
    "$$ E \\omega C R - D + F = 0 $$\n",
    "$$ E - B - F \\omega C R = -A $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "2a239e00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -Vc₂(t) \n",
       "──(Vc₁(t)) = ────────\n",
       "dt             C⋅R   "
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "e75ca38a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isinstance(eqn1, Equality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "31d5305e",
   "metadata": {},
   "outputs": [],
   "source": [
    "if isinstance(eqn1, Equality):\n",
    "    eq = eqn1.lhs - eqn1.rhs\n",
    "else:\n",
    "    eq = eqn1\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "6521fde3",
   "metadata": {},
   "outputs": [],
   "source": [
    "ii = 1\n",
    "for eqn in [eqn1, eqn2]:\n",
    "    sym1, sym2 = symbols('a_{} a_{}'.format(ii, ii+1))\n",
    "    vc = sym1*cos(w * t) + sym2 * sin(w*t)\n",
    "    eq = eqn.subs([])\n",
    "    \n",
    "    #display ([sym1, sym2])\n",
    "    ii += 2\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "c170de0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}C R \\omega & 0 & 0 & 1\\\\0 & - C R \\omega & 1 & 0\\\\0 & -1 & C R \\omega & 1\\\\-1 & 0 & 1 & - C R \\omega\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C⋅R⋅\\omega       0           0            1     ⎤\n",
       "⎢                                                ⎥\n",
       "⎢    0       -C⋅R⋅\\omega      1            0     ⎥\n",
       "⎢                                                ⎥\n",
       "⎢    0           -1       C⋅R⋅\\omega       1     ⎥\n",
       "⎢                                                ⎥\n",
       "⎣    -1           0           1       -C⋅R⋅\\omega⎦"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = Matrix([[w*C*R, 0, 0, 1], [0, -w*C*R, 1, 0], [0, -1, w*C*R, 1], [-1,0, 1, -w*C*R]])\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "e8cd9971",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C^{3} R^{3} \\omega^{3}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2} - 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2} - 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{2} R^{2} \\omega^{2} + 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{- C^{2} R^{2} \\omega^{2} + 1}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡           3  3       3                                                       ↪\n",
       "⎢          C ⋅R ⋅\\omega                             1                          ↪\n",
       "⎢─────────────────────────────────  ─────────────────────────────────  ─────── ↪\n",
       "⎢ 4  4       4    2  2       2       4  4       4    2  2       2       4  4   ↪\n",
       "⎢C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\ ↪\n",
       "⎢                                                                              ↪\n",
       "⎢                                              3  3       3                    ↪\n",
       "⎢                1                           -C ⋅R ⋅\\omega                     ↪\n",
       "⎢─────────────────────────────────  ─────────────────────────────────  ─────── ↪\n",
       "⎢ 4  4       4    2  2       2       4  4       4    2  2       2       4  4   ↪\n",
       "⎢C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\ ↪\n",
       "⎢                                                                              ↪\n",
       "⎢                                             2  2       2                 3   ↪\n",
       "⎢           C⋅R⋅\\omega                     - C ⋅R ⋅\\omega  + 1            C ⋅R ↪\n",
       "⎢─────────────────────────────────  ─────────────────────────────────  ─────── ↪\n",
       "⎢ 4  4       4    2  2       2       4  4       4    2  2       2       4  4   ↪\n",
       "⎢C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\ ↪\n",
       "⎢                                                                              ↪\n",
       "⎢          2  2       2                                                        ↪\n",
       "⎢       - C ⋅R ⋅\\omega  + 1                   -C⋅R⋅\\omega                      ↪\n",
       "⎢─────────────────────────────────  ─────────────────────────────────  ─────── ↪\n",
       "⎢ 4  4       4    2  2       2       4  4       4    2  2       2       4  4   ↪\n",
       "⎣C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\ ↪\n",
       "\n",
       "↪                                      2  2       2            ⎤\n",
       "↪    -C⋅R⋅\\omega                      C ⋅R ⋅\\omega  - 1        ⎥\n",
       "↪ ──────────────────────────  ─────────────────────────────────⎥\n",
       "↪      4    2  2       2       4  4       4    2  2       2    ⎥\n",
       "↪ omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1⎥\n",
       "↪                                                              ⎥\n",
       "↪   2  2       2                                               ⎥\n",
       "↪  C ⋅R ⋅\\omega  - 1                     C⋅R⋅\\omega            ⎥\n",
       "↪ ──────────────────────────  ─────────────────────────────────⎥\n",
       "↪      4    2  2       2       4  4       4    2  2       2    ⎥\n",
       "↪ omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1⎥\n",
       "↪                                                              ⎥\n",
       "↪ 3       3                              2  2       2          ⎥\n",
       "↪  ⋅\\omega  - C⋅R⋅\\omega                C ⋅R ⋅\\omega           ⎥\n",
       "↪ ──────────────────────────  ─────────────────────────────────⎥\n",
       "↪      4    2  2       2       4  4       4    2  2       2    ⎥\n",
       "↪ omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1⎥\n",
       "↪                                                              ⎥\n",
       "↪     2  2       2                 3  3       3                ⎥\n",
       "↪    C ⋅R ⋅\\omega               - C ⋅R ⋅\\omega  + C⋅R⋅\\omega   ⎥\n",
       "↪ ──────────────────────────  ─────────────────────────────────⎥\n",
       "↪      4    2  2       2       4  4       4    2  2       2    ⎥\n",
       "↪ omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1⎦"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minv = m**-1\n",
    "minv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "2c252f1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\- A\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0 ⎤\n",
       "⎢  ⎥\n",
       "⎢0 ⎥\n",
       "⎢  ⎥\n",
       "⎢0 ⎥\n",
       "⎢  ⎥\n",
       "⎣-A⎦"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "amat = Matrix([0,0,0,-A])\n",
    "amat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "4a5efba9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡        ⎛ 2  2       2    ⎞       ⎤\n",
       "⎢     -A⋅⎝C ⋅R ⋅\\omega  - 1⎠       ⎥\n",
       "⎢───────────────────────────────── ⎥\n",
       "⎢ 4  4       4    2  2       2     ⎥\n",
       "⎢C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1 ⎥\n",
       "⎢                                  ⎥\n",
       "⎢         -A⋅C⋅R⋅\\omega            ⎥\n",
       "⎢───────────────────────────────── ⎥\n",
       "⎢ 4  4       4    2  2       2     ⎥\n",
       "⎢C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1 ⎥\n",
       "⎢                                  ⎥\n",
       "⎢            2  2       2          ⎥\n",
       "⎢        -A⋅C ⋅R ⋅\\omega           ⎥\n",
       "⎢───────────────────────────────── ⎥\n",
       "⎢ 4  4       4    2  2       2     ⎥\n",
       "⎢C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1 ⎥\n",
       "⎢                                  ⎥\n",
       "⎢   ⎛   3  3       3             ⎞ ⎥\n",
       "⎢-A⋅⎝- C ⋅R ⋅\\omega  + C⋅R⋅\\omega⎠ ⎥\n",
       "⎢──────────────────────────────────⎥\n",
       "⎢ 4  4       4    2  2       2     ⎥\n",
       "⎣C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1 ⎦"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the coefficients of B,D,E and F.\n",
    "coeffs = minv*amat\n",
    "coeffs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "7edafd6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( - \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\  - \\frac{A C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\  - \\frac{A C R \\omega}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}, \\  - \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}\\right)$"
      ],
      "text/plain": [
       "⎛        ⎛ 2  2       2    ⎞                    2  2       2                   ↪\n",
       "⎜     -A⋅⎝C ⋅R ⋅\\omega  - 1⎠                -A⋅C ⋅R ⋅\\omega                    ↪\n",
       "⎜─────────────────────────────────, ─────────────────────────────────, ─────── ↪\n",
       "⎜ 4  4       4    2  2       2       4  4       4    2  2       2       4  4   ↪\n",
       "⎝C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\ ↪\n",
       "\n",
       "↪                                ⎛   3  3       3             ⎞ ⎞\n",
       "↪   -A⋅C⋅R⋅\\omega             -A⋅⎝- C ⋅R ⋅\\omega  + C⋅R⋅\\omega⎠ ⎟\n",
       "↪ ──────────────────────────, ──────────────────────────────────⎟\n",
       "↪      4    2  2       2       4  4       4    2  2       2     ⎟\n",
       "↪ omega  - C ⋅R ⋅\\omega  + 1  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1 ⎠"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = coeffs[0]\n",
    "d = coeffs[1]\n",
    "e = coeffs[2]\n",
    "f = coeffs[3]\n",
    "b, e, d, f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "15bfbe9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(f + b * w* C* R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "2274eae6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = eq1.subs([(B,b), (D,d), (E,e), (F,f)]).doit()\n",
    "simplify(eq.lhs - eq.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "47d3a7eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = eq2.subs([(B,b), (D,d), (E,e), (F,f)]).doit()\n",
    "simplify(eq.lhs - eq.rhs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "1e658941",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} - \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right) \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "                                        ⎛ 2  2       2    ⎞              \n",
       "     A⋅C⋅R⋅\\omega⋅cos(\\omega⋅t)       A⋅⎝C ⋅R ⋅\\omega  - 1⎠⋅sin(\\omega⋅t)\n",
       "- ───────────────────────────────── - ───────────────────────────────────\n",
       "   4  4       4    2  2       2         4  4       4    2  2       2     \n",
       "  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1    C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1 "
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vc1.subs([(B,b),(D,d)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "21799d72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} - \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right) \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "       2  2       2                     ⎛   3  3       3             ⎞         ↪\n",
       "    A⋅C ⋅R ⋅\\omega ⋅sin(\\omega⋅t)     A⋅⎝- C ⋅R ⋅\\omega  + C⋅R⋅\\omega⎠⋅cos(\\om ↪\n",
       "- ───────────────────────────────── - ──────────────────────────────────────── ↪\n",
       "   4  4       4    2  2       2              4  4       4    2  2       2      ↪\n",
       "  C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1         C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1  ↪\n",
       "\n",
       "↪       \n",
       "↪ ega⋅t)\n",
       "↪ ──────\n",
       "↪       \n",
       "↪       "
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vc2.subs([(E,e), (F,f)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "8d622a8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "                2                \n",
       "               A                 \n",
       "─────────────────────────────────\n",
       " 4  4       4    2  2       2    \n",
       "C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the magnitude of Vc1\n",
    "simplify(b**2+d**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "37d264fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A^{2} C^{2} R^{2} \\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "         2  2  2       2         \n",
       "        A ⋅C ⋅R ⋅\\omega          \n",
       "─────────────────────────────────\n",
       " 4  4       4    2  2       2    \n",
       "C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the magnitude of Vc2\n",
    "(simplify(e**2+f**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "096e59a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\phi = \\operatorname{acos}{\\left(C R \\sqrt{\\frac{\\omega^{2}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}} \\right)}$"
      ],
      "text/plain": [
       "        ⎛          ___________________________________⎞\n",
       "        ⎜         ╱                    2              ⎟\n",
       "        ⎜        ╱               \\omega               ⎟\n",
       "φ = acos⎜C⋅R⋅   ╱   ───────────────────────────────── ⎟\n",
       "        ⎜      ╱     4  4       4    2  2       2     ⎟\n",
       "        ⎝    ╲╱     C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1 ⎠"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now compute phase of Vc1\n",
    "Eq(phi, acos(sqrt(simplify(d**2/(b**2+d**2)))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "bc3d128f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\phi = \\operatorname{acos}{\\left(\\sqrt{\\frac{\\left(C^{2} R^{2} \\omega^{2} - 1\\right)^{2}}{C^{2} R^{2} \\omega^{2} + \\left(C^{2} R^{2} \\omega^{2} - 1\\right)^{2}}} \\right)}$"
      ],
      "text/plain": [
       "        ⎛        ______________________________________⎞\n",
       "        ⎜       ╱                            2         ⎟\n",
       "        ⎜      ╱          ⎛ 2  2       2    ⎞          ⎟\n",
       "        ⎜     ╱           ⎝C ⋅R ⋅\\omega  - 1⎠          ⎟\n",
       "φ = acos⎜    ╱    ──────────────────────────────────── ⎟\n",
       "        ⎜   ╱                                        2 ⎟\n",
       "        ⎜  ╱       2  2       2   ⎛ 2  2       2    ⎞  ⎟\n",
       "        ⎝╲╱       C ⋅R ⋅\\omega  + ⎝C ⋅R ⋅\\omega  - 1⎠  ⎠"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now compute phase of Vc2\n",
    "Eq(phi, acos(sqrt(simplify(f**2/(e**2+f**2)))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "5f98d6e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{C R \\omega}{C^{2} R^{2} \\omega^{2} - 1}$"
      ],
      "text/plain": [
       "   C⋅R⋅\\omega    \n",
       "─────────────────\n",
       " 2  2       2    \n",
       "C ⋅R ⋅\\omega  - 1"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I am have a bit of a guess here at computing  tan (phi)\n",
    "d/b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "038f993b-ac01-4eef-bf57-9c4dd68f21ca",
   "metadata": {},
   "source": [
    "### Compute V_R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "cd55f6cb-560b-4171-b48e-8fa3850c2b27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + \\frac{A C R \\omega \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{2} R^{2} \\omega^{2} - 1\\right) \\sin{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{3} R^{3} \\omega^{3} + C R \\omega\\right) \\cos{\\left(\\omega t \\right)}}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1} + A \\sin{\\left(\\omega t \\right)}$"
      ],
      "text/plain": [
       "     2  2       2                                                         ⎛ 2  ↪\n",
       "  A⋅C ⋅R ⋅\\omega ⋅sin(\\omega⋅t)        A⋅C⋅R⋅\\omega⋅cos(\\omega⋅t)       A⋅⎝C ⋅ ↪\n",
       "───────────────────────────────── + ───────────────────────────────── + ────── ↪\n",
       " 4  4       4    2  2       2        4  4       4    2  2       2         4  4 ↪\n",
       "C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1   C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1    C ⋅R  ↪\n",
       "\n",
       "↪  2       2    ⎞                   ⎛   3  3       3             ⎞             ↪\n",
       "↪ R ⋅\\omega  - 1⎠⋅sin(\\omega⋅t)   A⋅⎝- C ⋅R ⋅\\omega  + C⋅R⋅\\omega⎠⋅cos(\\omega⋅ ↪\n",
       "↪ ───────────────────────────── + ──────────────────────────────────────────── ↪\n",
       "↪        4    2  2       2               4  4       4    2  2       2          ↪\n",
       "↪ ⋅\\omega  - C ⋅R ⋅\\omega  + 1          C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1      ↪\n",
       "\n",
       "↪                     \n",
       "↪ t)                  \n",
       "↪ ── + A⋅sin(\\omega⋅t)\n",
       "↪                     \n",
       "↪                     "
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vr = A*sin(w*t) - b* sin(w*t) - d*cos(w*t) - e*sin(w*t) - f*cos(w*t)\n",
    "vr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "db9bbd1f-00f1-4981-a8fb-7417eb6d69f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega \\left(C^{3} R^{3} \\omega^{3} \\sin{\\left(\\omega t \\right)} - C^{2} R^{2} \\omega^{2} \\cos{\\left(\\omega t \\right)} + C R \\omega \\sin{\\left(\\omega t \\right)} + 2 \\cos{\\left(\\omega t \\right)}\\right)}{C^{4} R^{4} \\omega^{4} - C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "             ⎛ 3  3       3                  2  2       2                      ↪\n",
       "A⋅C⋅R⋅\\omega⋅⎝C ⋅R ⋅\\omega ⋅sin(\\omega⋅t) - C ⋅R ⋅\\omega ⋅cos(\\omega⋅t) + C⋅R⋅ ↪\n",
       "────────────────────────────────────────────────────────────────────────────── ↪\n",
       "                                           4  4       4    2  2       2        ↪\n",
       "                                          C ⋅R ⋅\\omega  - C ⋅R ⋅\\omega  + 1    ↪\n",
       "\n",
       "↪                                       ⎞\n",
       "↪ \\omega⋅sin(\\omega⋅t) + 2⋅cos(\\omega⋅t)⎠\n",
       "↪ ───────────────────────────────────────\n",
       "↪                                        \n",
       "↪                                        "
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(vr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9952df1c",
   "metadata": {},
   "source": [
    "## Larger (x 3) RC Network \n",
    "Now try the same thing with three lots of RC components\n",
    "\n",
    "There are three equations:\n",
    "\n",
    "$$ A \\sin ( \\omega t ) - V_{C1} - R_1 (i_1 - i_2) = 0 $$\n",
    "$$ R_1 ( i_2 - i_1) - V_{C2} - R_2 (i_2 - i_3) = 0 $$\n",
    "$$ R_2 ( i_3 - i_2) - V_{C3} - R_3 i_3 = 0 $$\n",
    "//\n",
    "These can be rearranged so that all the i's are on the right and everything else on the left.\n",
    "\n",
    "$$ A \\sin ( \\omega t ) - V_{C1} = R_1 i_1 - R_1 i_2 $$\n",
    "$$  V_{C2} = R_1 ( i_2 - i_1) -  R_2 (i_2 - i_3) = (R_1 - R_2) i_2 - R_1 i_1 - R_2 i_3 $$\n",
    "$$  V_{C3} = R_2 ( i_3 - i_2) -  R_3 i_3 = (R_2 - R_3) i_3 - R_2 i_2 $$\n",
    "\n",
    "However if R1 = R2 = R3 the above simplifies to :\n",
    "\n",
    "$$ A \\sin ( \\omega t ) - V_{C1} = R i_1 - R i_2 $$\n",
    "$$  V_{C2} = - R i_1 - R i_3 $$\n",
    "$$  V_{C3} = - R i_2 $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2af0f0fe-a18d-4389-bc4f-cd993060ba27",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "be3953e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}R & - R & 0\\\\- R & 0 & - R\\\\0 & - R & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡R   -R  0 ⎤\n",
       "⎢          ⎥\n",
       "⎢-R  0   -R⎥\n",
       "⎢          ⎥\n",
       "⎣0   -R  0 ⎦"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = Matrix([[R, -R, 0], [-R, 0, -R], [0, -R, 0]]); m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "989e65a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle - R^{3}$"
      ],
      "text/plain": [
       "  3\n",
       "-R "
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "8e0a402b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\\\operatorname{Vc}_{2}{\\left(t \\right)}\\\\\\operatorname{Vc}_{3}{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡A⋅sin(\\omega⋅t) - Vc₁(t)⎤\n",
       "⎢                        ⎥\n",
       "⎢         Vc₂(t)         ⎥\n",
       "⎢                        ⎥\n",
       "⎣         Vc₃(t)         ⎦"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Matrix([A*sin(w*t)-Vc1(t), Vc2(t), Vc3(t)]);v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "d94e3e61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{R} & 0 & - \\frac{1}{R}\\\\0 & 0 & - \\frac{1}{R}\\\\- \\frac{1}{R} & - \\frac{1}{R} & \\frac{1}{R}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ 1        -1 ⎤\n",
       "⎢ ─    0   ───⎥\n",
       "⎢ R         R ⎥\n",
       "⎢             ⎥\n",
       "⎢          -1 ⎥\n",
       "⎢ 0    0   ───⎥\n",
       "⎢           R ⎥\n",
       "⎢             ⎥\n",
       "⎢-1   -1    1 ⎥\n",
       "⎢───  ───   ─ ⎥\n",
       "⎣ R    R    R ⎦"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "bbeeee6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R} - \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\\\- \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\\\- \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)}}{R} - \\frac{\\operatorname{Vc}_{2}{\\left(t \\right)}}{R} + \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{R}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡     A⋅sin(\\omega⋅t) - Vc₁(t)   Vc₃(t)      ⎤\n",
       "⎢     ──────────────────────── - ──────      ⎥\n",
       "⎢                R                 R         ⎥\n",
       "⎢                                            ⎥\n",
       "⎢                  -Vc₃(t)                   ⎥\n",
       "⎢                  ────────                  ⎥\n",
       "⎢                     R                      ⎥\n",
       "⎢                                            ⎥\n",
       "⎢  A⋅sin(\\omega⋅t) - Vc₁(t)   Vc₂(t)   Vc₃(t)⎥\n",
       "⎢- ──────────────────────── - ────── + ──────⎥\n",
       "⎣             R                 R        R   ⎦"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now to calculate the currents i1, i2, i3\n",
    "minvv = m.inv()*v; minvv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "e51811ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "Vc1 = Function('Vc1')\n",
    "Vc2 = Function('Vc2')\n",
    "Vc3 = Function('Vc3')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "8902fcbd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}C \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)}\\\\C \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)}\\\\C \\frac{d}{d t} \\operatorname{Vc}_{3}{\\left(t \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  d         ⎤\n",
       "⎢C⋅──(Vc₁(t))⎥\n",
       "⎢  dt        ⎥\n",
       "⎢            ⎥\n",
       "⎢  d         ⎥\n",
       "⎢C⋅──(Vc₂(t))⎥\n",
       "⎢  dt        ⎥\n",
       "⎢            ⎥\n",
       "⎢  d         ⎥\n",
       "⎢C⋅──(Vc₃(t))⎥\n",
       "⎣  dt        ⎦"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mm = Matrix([C*Vc1(t).diff(), C*Vc2(t).diff(), C*Vc3(t).diff()]); mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "28aa249b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            A⋅sin(\\omega⋅t) - Vc₁(t) - Vc₃(t)\n",
       "──(Vc₁(t)) = ─────────────────────────────────\n",
       "dt                          C⋅R               "
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn1 = Eq(mm[0]/C, simplify(minvv[0]/C)); eqn1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "717505e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{1}{\\left(t \\right)} = \\frac{A \\sin{\\left(\\omega t \\right)} - \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            A⋅sin(\\omega⋅t) - Vc₁(t) - Vc₃(t)\n",
       "──(Vc₁(t)) = ─────────────────────────────────\n",
       "dt                          C⋅R               "
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "ea323a49",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(Derivative(Vc1(t), t), (A*sin(\\omega*t) - Vc1(t) - Vc3(t))/(C*R))\n"
     ]
    }
   ],
   "source": [
    "print(eqn1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "e74d9997",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{2}{\\left(t \\right)} = - \\frac{\\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -Vc₃(t) \n",
       "──(Vc₂(t)) = ────────\n",
       "dt             C⋅R   "
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn2 = Eq(mm[1]/C, simplify(minvv[1]/C)); eqn2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "2875b41c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(Derivative(Vc2(t), t), -Vc3(t)/(C*R))\n"
     ]
    }
   ],
   "source": [
    "print(eqn2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "8066a383",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} \\operatorname{Vc}_{3}{\\left(t \\right)} = \\frac{- A \\sin{\\left(\\omega t \\right)} + \\operatorname{Vc}_{1}{\\left(t \\right)} - \\operatorname{Vc}_{2}{\\left(t \\right)} + \\operatorname{Vc}_{3}{\\left(t \\right)}}{C R}$"
      ],
      "text/plain": [
       "d            -A⋅sin(\\omega⋅t) + Vc₁(t) - Vc₂(t) + Vc₃(t)\n",
       "──(Vc₃(t)) = ───────────────────────────────────────────\n",
       "dt                               C⋅R                    "
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eqn3 = Eq(mm[2]/C, simplify(minvv[2]/C)); eqn3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "c23c9ce7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(Derivative(Vc3(t), t), (-A*sin(\\omega*t) + Vc1(t) - Vc2(t) + Vc3(t))/(C*R))\n"
     ]
    }
   ],
   "source": [
    "print(eqn3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "55da3b94",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(a_2*omega, -a_1*omega), (a_1/(C*R), a_2/(C*R)), (a_3/(C*R), a_4/(C*R)), (0, -A*a_6/(C*R))]\n",
      "[(a_8*omega, -a_7*omega), (a_3/(C*R), a_4/(C*R))]\n",
      "[(a_4*omega, -a_3*omega), (-a_1/(C*R), -a_2/(C*R)), (-a_3/(C*R), -a_4/(C*R)), (a_7/(C*R), a_8/(C*R)), (0, A*a_6/(C*R))]\n",
      "[a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8]\n"
     ]
    }
   ],
   "source": [
    "sysEqns3 = systemEqns()\n",
    "\n",
    "res1 = sysEqns3.extractCoeffsFromDiffEqn(eqn1)\n",
    "print (res1)\n",
    "res2 = sysEqns3.extractCoeffsFromDiffEqn(eqn2)\n",
    "print (res2)\n",
    "res3 = sysEqns3.extractCoeffsFromDiffEqn(eqn3)\n",
    "print (res3)\n",
    "\n",
    "print (sysEqns3.symbols_used)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "bb3c1ceb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\omega & \\frac{1}{C R} & 0 & 0 & 0 & \\frac{1}{C R} & 0 & - \\frac{A}{C R}\\\\\\frac{1}{C R} & \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & 0 & - \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & 0 & 0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & 0 & \\frac{1}{C R} & - \\omega & - \\frac{1}{C R} & 0 & \\frac{A}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & 0 & - \\frac{1}{C R} & \\omega & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡      1                   1      -A ⎤\n",
       "⎢-ω   ───   0    0    0   ───  0  ───⎥\n",
       "⎢     C⋅R                 C⋅R     C⋅R⎥\n",
       "⎢                                    ⎥\n",
       "⎢ 1                   1              ⎥\n",
       "⎢───   ω    0    0   ───   0   0   0 ⎥\n",
       "⎢C⋅R                 C⋅R             ⎥\n",
       "⎢                                    ⎥\n",
       "⎢                          1         ⎥\n",
       "⎢ 0    0   -ω    0    0   ───  0   0 ⎥\n",
       "⎢                         C⋅R        ⎥\n",
       "⎢                                    ⎥\n",
       "⎢                     1              ⎥\n",
       "⎢ 0    0    0    ω   ───   0   0   0 ⎥\n",
       "⎢                    C⋅R             ⎥\n",
       "⎢                                    ⎥\n",
       "⎢     -1         1        -1       A ⎥\n",
       "⎢ 0   ───   0   ───  -ω   ───  0  ───⎥\n",
       "⎢     C⋅R       C⋅R       C⋅R     C⋅R⎥\n",
       "⎢                                    ⎥\n",
       "⎢-1         1        -1              ⎥\n",
       "⎢───   0   ───   0   ───   ω   0   0 ⎥\n",
       "⎣C⋅R       C⋅R       C⋅R             ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M, syms_used = sysEqns3.orderedMatrix([res1, res2, res3])\n",
    "display(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "66d5c346",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left[ a_{1}, \\  a_{2}, \\  a_{7}, \\  a_{8}, \\  a_{3}, \\  a_{4}, \\  a_{5}, \\  a_{6}\\right]$"
      ],
      "text/plain": [
       "[a₁, a₂, a₇, a₈, a₃, a₄, a₅, a₆]"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "syms_used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "9006121e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\omega & \\frac{1}{C R} & 0 & 0 & 0 & \\frac{1}{C R} & 0 & - \\frac{A}{C R}\\\\\\frac{1}{C R} & \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & 0 & - \\omega & 0 & 0 & \\frac{1}{C R} & 0 & 0\\\\0 & 0 & 0 & \\omega & \\frac{1}{C R} & 0 & 0 & 0\\\\0 & - \\frac{1}{C R} & 0 & \\frac{1}{C R} & - \\omega & - \\frac{1}{C R} & 0 & \\frac{A}{C R}\\\\- \\frac{1}{C R} & 0 & \\frac{1}{C R} & 0 & - \\frac{1}{C R} & \\omega & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡      1                   1      -A ⎤\n",
       "⎢-ω   ───   0    0    0   ───  0  ───⎥\n",
       "⎢     C⋅R                 C⋅R     C⋅R⎥\n",
       "⎢                                    ⎥\n",
       "⎢ 1                   1              ⎥\n",
       "⎢───   ω    0    0   ───   0   0   0 ⎥\n",
       "⎢C⋅R                 C⋅R             ⎥\n",
       "⎢                                    ⎥\n",
       "⎢                          1         ⎥\n",
       "⎢ 0    0   -ω    0    0   ───  0   0 ⎥\n",
       "⎢                         C⋅R        ⎥\n",
       "⎢                                    ⎥\n",
       "⎢                     1              ⎥\n",
       "⎢ 0    0    0    ω   ───   0   0   0 ⎥\n",
       "⎢                    C⋅R             ⎥\n",
       "⎢                                    ⎥\n",
       "⎢     -1         1        -1       A ⎥\n",
       "⎢ 0   ───   0   ───  -ω   ───  0  ───⎥\n",
       "⎢     C⋅R       C⋅R       C⋅R     C⋅R⎥\n",
       "⎢                                    ⎥\n",
       "⎢-1         1        -1              ⎥\n",
       "⎢───   0   ───   0   ───   ω   0   0 ⎥\n",
       "⎣C⋅R       C⋅R       C⋅R             ⎦"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "2a72d91f",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "#M_1 = M[:6,:6]**-1; M_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "7eca5f0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\left( 6, \\  8\\right)$"
      ],
      "text/plain": [
       "(6, 8)"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "20d74c31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}C R \\omega & -1 & 0 & 0 & 0 & -1 & 0 & A\\\\-1 & - C R \\omega & 0 & 0 & -1 & 0 & 0 & 0\\\\0 & 0 & - C R \\omega & 0 & 0 & 1 & 0 & 0\\\\0 & 0 & 0 & C R \\omega & 1 & 0 & 0 & 0\\\\0 & -1 & 0 & 1 & - C R \\omega & -1 & 0 & A\\\\-1 & 0 & 1 & 0 & -1 & C R \\omega & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C⋅R⋅ω    -1      0       0      0      -1    0  A⎤\n",
       "⎢                                                 ⎥\n",
       "⎢ -1    -C⋅R⋅ω    0       0      -1      0    0  0⎥\n",
       "⎢                                                 ⎥\n",
       "⎢  0      0     -C⋅R⋅ω    0      0       1    0  0⎥\n",
       "⎢                                                 ⎥\n",
       "⎢  0      0       0     C⋅R⋅ω    1       0    0  0⎥\n",
       "⎢                                                 ⎥\n",
       "⎢  0      -1      0       1    -C⋅R⋅ω   -1    0  A⎥\n",
       "⎢                                                 ⎥\n",
       "⎣ -1      0       1       0      -1    C⋅R⋅ω  0  0⎦"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the method row_op on the matrix to multiply the whole matrix through by a prefactor\n",
    "\n",
    "# I also did a bit of fiddling with the signs of the first two rows of the matrix by also swapping\n",
    "# it's signs on the basis that if I multiply any equation through by a constant it shouldn't matter.  The\n",
    "# same principle as for the rest of the rows really.\n",
    "#\n",
    "M2 = M.copy()\n",
    "for ii in range(6):\n",
    "    if ii < 2:\n",
    "        M2.row_op(ii, lambda e, col: -e*R*C)\n",
    "    else:\n",
    "        M2.row_op(ii, lambda e, col: e*R*C)\n",
    "\n",
    "M2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "dc5fc471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}C R \\omega & -1 & 0 & 0 & 0 & -1\\\\-1 & - C R \\omega & 0 & 0 & -1 & 0\\\\0 & 0 & - C R \\omega & 0 & 0 & 1\\\\0 & 0 & 0 & C R \\omega & 1 & 0\\\\0 & -1 & 0 & 1 & - C R \\omega & -1\\\\-1 & 0 & 1 & 0 & -1 & C R \\omega\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡C⋅R⋅ω    -1      0       0      0      -1  ⎤\n",
       "⎢                                           ⎥\n",
       "⎢ -1    -C⋅R⋅ω    0       0      -1      0  ⎥\n",
       "⎢                                           ⎥\n",
       "⎢  0      0     -C⋅R⋅ω    0      0       1  ⎥\n",
       "⎢                                           ⎥\n",
       "⎢  0      0       0     C⋅R⋅ω    1       0  ⎥\n",
       "⎢                                           ⎥\n",
       "⎢  0      -1      0       1    -C⋅R⋅ω   -1  ⎥\n",
       "⎢                                           ⎥\n",
       "⎣ -1      0       1       0      -1    C⋅R⋅ω⎦"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3 = M2[:6,:6]\n",
    "M3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "1b70eefa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{C^{5} R^{5} \\omega^{5} + 2 C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - 2 C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{5} R^{5} \\omega^{5} + C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3} - C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & - \\frac{C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} & \\frac{C^{5} R^{5} \\omega^{5} + C^{3} R^{3} \\omega^{3} + C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡        5  5  5      3  3  3                 4  4  4      2  2  2             ↪\n",
       "⎢       C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω               - C ⋅R ⋅ω  - 2⋅C ⋅R ⋅ω  - 1         ↪\n",
       "⎢────────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "⎢ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "⎢C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "⎢                                                                              ↪\n",
       "⎢       4  4  4      2  2  2                    5  5  5      3  3  3           ↪\n",
       "⎢    - C ⋅R ⋅ω  - 2⋅C ⋅R ⋅ω  - 1             - C ⋅R ⋅ω  - 2⋅C ⋅R ⋅ω            ↪\n",
       "⎢────────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "⎢ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "⎢C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "⎢                                                                              ↪\n",
       "⎢           3  3  3                                                            ↪\n",
       "⎢          C ⋅R ⋅ω  + C⋅R⋅ω                            -1                      ↪\n",
       "⎢────────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "⎢ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "⎢C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "⎢                                                                              ↪\n",
       "⎢                                                  3  3  3                     ↪\n",
       "⎢                -1                             - C ⋅R ⋅ω  - C⋅R⋅ω             ↪\n",
       "⎢────────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "⎢ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "⎢C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "⎢                                                                              ↪\n",
       "⎢                                               4  4  4    2  2  2             ↪\n",
       "⎢               C⋅R⋅ω                          C ⋅R ⋅ω  + C ⋅R ⋅ω              ↪\n",
       "⎢────────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "⎢ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "⎢C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "⎢                                                                              ↪\n",
       "⎢         4  4  4    2  2  2                                                   ↪\n",
       "⎢        C ⋅R ⋅ω  + C ⋅R ⋅ω                          -C⋅R⋅ω                    ↪\n",
       "⎢────────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "⎢ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "⎣C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "\n",
       "↪           3  3  3                                                            ↪\n",
       "↪          C ⋅R ⋅ω  + C⋅R⋅ω                            -1                      ↪\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "↪                                                                              ↪\n",
       "↪                                                  3  3  3                     ↪\n",
       "↪                -1                             - C ⋅R ⋅ω  - C⋅R⋅ω             ↪\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "↪                                                                              ↪\n",
       "↪          5  5  5    3  3  3                         2  2  2                  ↪\n",
       "↪       - C ⋅R ⋅ω  - C ⋅R ⋅ω                         C ⋅R ⋅ω                   ↪\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "↪                                                                              ↪\n",
       "↪               2  2  2                         5  5  5    3  3  3             ↪\n",
       "↪              C ⋅R ⋅ω                         C ⋅R ⋅ω  + C ⋅R ⋅ω              ↪\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "↪                                                                              ↪\n",
       "↪               3  3  3                       4  4  4    2  2  2               ↪\n",
       "↪             -C ⋅R ⋅ω                       C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1           ↪\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "↪                                                                              ↪\n",
       "↪       4  4  4    2  2  2                            3  3  3                  ↪\n",
       "↪      C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1                       C ⋅R ⋅ω                   ↪\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────  ─ ↪\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2        ↪\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ↪\n",
       "\n",
       "↪                                               4  4  4    2  2  2         ⎤\n",
       "↪               C⋅R⋅ω                          C ⋅R ⋅ω  + C ⋅R ⋅ω          ⎥\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────⎥\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2    ⎥\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎥\n",
       "↪                                                                          ⎥\n",
       "↪         4  4  4    2  2  2                                               ⎥\n",
       "↪        C ⋅R ⋅ω  + C ⋅R ⋅ω                          -C⋅R⋅ω                ⎥\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────⎥\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2    ⎥\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎥\n",
       "↪                                                                          ⎥\n",
       "↪               3  3  3                       4  4  4    2  2  2           ⎥\n",
       "↪             -C ⋅R ⋅ω                       C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1       ⎥\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────⎥\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2    ⎥\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎥\n",
       "↪                                                                          ⎥\n",
       "↪       4  4  4    2  2  2                            3  3  3              ⎥\n",
       "↪      C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1                       C ⋅R ⋅ω               ⎥\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────⎥\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2    ⎥\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎥\n",
       "↪                                                                          ⎥\n",
       "↪      5  5  5    3  3  3                             4  4  4              ⎥\n",
       "↪   - C ⋅R ⋅ω  - C ⋅R ⋅ω  - C⋅R⋅ω                   -C ⋅R ⋅ω               ⎥\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────⎥\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2    ⎥\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎥\n",
       "↪                                                                          ⎥\n",
       "↪               4  4  4                     5  5  5    3  3  3             ⎥\n",
       "↪             -C ⋅R ⋅ω                     C ⋅R ⋅ω  + C ⋅R ⋅ω  + C⋅R⋅ω     ⎥\n",
       "↪ ───────────────────────────────────  ────────────────────────────────────⎥\n",
       "↪ 6  6  6      4  4  4    2  2  2       6  6  6      4  4  4    2  2  2    ⎥\n",
       "↪  ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎦"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M3**-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "2e9c93a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}A\\\\0\\\\0\\\\0\\\\A\\\\0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡A⎤\n",
       "⎢ ⎥\n",
       "⎢0⎥\n",
       "⎢ ⎥\n",
       "⎢0⎥\n",
       "⎢ ⎥\n",
       "⎢0⎥\n",
       "⎢ ⎥\n",
       "⎢A⎥\n",
       "⎢ ⎥\n",
       "⎣0⎦"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col = M2[:,7]\n",
    "col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "ad3c7583",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{5} R^{5} \\omega^{5} + 2 C^{3} R^{3} \\omega^{3}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{4} R^{4} \\omega^{4} - 2 C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{3} R^{3} \\omega^{3}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{3} R^{3} \\omega^{3} + C R \\omega\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} - \\frac{A}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\\\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(- C^{5} R^{5} \\omega^{5} - C^{3} R^{3} \\omega^{3} - C R \\omega\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\\\- \\frac{A C^{4} R^{4} \\omega^{4}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1} + \\frac{A \\left(C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2}\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                                               ⎛ 5  5  5      3  3  3⎞       ⎤\n",
       "⎢               A⋅C⋅R⋅ω                       A⋅⎝C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω ⎠       ⎥\n",
       "⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n",
       "⎢  6  6  6      4  4  4    2  2  2        6  6  6      4  4  4    2  2  2     ⎥\n",
       "⎢ C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1   C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1 ⎥\n",
       "⎢                                                                             ⎥\n",
       "⎢         ⎛ 4  4  4    2  2  2⎞              ⎛   4  4  4      2  2  2    ⎞    ⎥\n",
       "⎢       A⋅⎝C ⋅R ⋅ω  + C ⋅R ⋅ω ⎠            A⋅⎝- C ⋅R ⋅ω  - 2⋅C ⋅R ⋅ω  - 1⎠    ⎥\n",
       "⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n",
       "⎢  6  6  6      4  4  4    2  2  2        6  6  6      4  4  4    2  2  2     ⎥\n",
       "⎢ C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1   C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1 ⎥\n",
       "⎢                                                                             ⎥\n",
       "⎢                  3  3  3                          ⎛ 3  3  3        ⎞        ⎥\n",
       "⎢               A⋅C ⋅R ⋅ω                         A⋅⎝C ⋅R ⋅ω  + C⋅R⋅ω⎠        ⎥\n",
       "⎢- ──────────────────────────────────── + ────────────────────────────────────⎥\n",
       "⎢   6  6  6      4  4  4    2  2  2        6  6  6      4  4  4    2  2  2    ⎥\n",
       "⎢  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1   C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎥\n",
       "⎢                                                                             ⎥\n",
       "⎢       ⎛ 4  4  4    2  2  2    ⎞                                             ⎥\n",
       "⎢     A⋅⎝C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎠                         A                   ⎥\n",
       "⎢ ──────────────────────────────────── - ──────────────────────────────────── ⎥\n",
       "⎢  6  6  6      4  4  4    2  2  2        6  6  6      4  4  4    2  2  2     ⎥\n",
       "⎢ C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1   C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1 ⎥\n",
       "⎢                                                                             ⎥\n",
       "⎢                                           ⎛   5  5  5    3  3  3        ⎞   ⎥\n",
       "⎢               A⋅C⋅R⋅ω                   A⋅⎝- C ⋅R ⋅ω  - C ⋅R ⋅ω  - C⋅R⋅ω⎠   ⎥\n",
       "⎢ ──────────────────────────────────── + ──────────────────────────────────── ⎥\n",
       "⎢  6  6  6      4  4  4    2  2  2        6  6  6      4  4  4    2  2  2     ⎥\n",
       "⎢ C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1   C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1 ⎥\n",
       "⎢                                                                             ⎥\n",
       "⎢                  4  4  4                        ⎛ 4  4  4    2  2  2⎞       ⎥\n",
       "⎢               A⋅C ⋅R ⋅ω                       A⋅⎝C ⋅R ⋅ω  + C ⋅R ⋅ω ⎠       ⎥\n",
       "⎢- ──────────────────────────────────── + ────────────────────────────────────⎥\n",
       "⎢   6  6  6      4  4  4    2  2  2        6  6  6      4  4  4    2  2  2    ⎥\n",
       "⎣  C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1   C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1⎦"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = M3**-1*col\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "599f7599",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega \\left(C^{2} R^{2} \\omega^{2} \\left(C^{2} R^{2} \\omega^{2} + 2\\right) + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "        ⎛ 2  2  2 ⎛ 2  2  2    ⎞    ⎞\n",
       "A⋅C⋅R⋅ω⋅⎝C ⋅R ⋅ω ⋅⎝C ⋅R ⋅ω  + 2⎠ + 1⎠\n",
       "─────────────────────────────────────\n",
       " 6  6  6      4  4  4    2  2  2     \n",
       "C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1 "
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(res[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "8830a26f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A \\left(- C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "           ⎛   2  2  2    ⎞         \n",
       "         A⋅⎝- C ⋅R ⋅ω  - 1⎠         \n",
       "────────────────────────────────────\n",
       " 6  6  6      4  4  4    2  2  2    \n",
       "C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(res[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "3bd9f332",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOkAAAAfCAYAAAAC/OrnAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuNSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/xnp5ZAAAACXBIWXMAABJ0AAASdAHeZh94AAAHQElEQVR4nO2cb4xdRRnGf61FQi1qiaBoNBKtjQXDdtco/wQkFqMhAYmImDSWD5KmCUK0xbQYHh9NkFRhqURjgzEb4YMGDEZMC1QgwQqYNkChCCG1khqVmFiwrCimdP0wc9qzt/eeO+f+2Xs+zC/Z3HvnzHnO3PfO7DvnzLzvvJmZGTKZTHNZMOoGZGZj+8PAk8DzksbaHB8D1gHnAe8A/g7sBDZK2hHrPAhcEE85CLwYj98+5OZnhsD8UTcgcxQ/AG4Bltl+c/mA7VWEAfk6cDnwIeDL8fPqUtVxYANwMvBB4OfAZtvLh934zODJnrRB2L6U8I9zI7AeWAY8FY+dCfwEWCdpsnTaPuAR2yfEeh8A3g7cJ+mlWLYZ+CZwKsFLF9ebBD4BfEzSoZa27AS2S7p20N8zU4/sSRuC7eOA7wNrJb0C/A0oe76bgT+0DNDDSNof304AB4BdUffkqHsIeKJ0vaXA1YRBf4ijea7l+pkRkT1pc/gGwXMVnu5ZYAzA9hLgTOCKBJ0JYBFwwPZ84Djgf8DXJf2xVG8tsEvSwx109gMfr/slMoMne9IGYPv9wFeB60vFuzniycbj684EuXHCtHgMOAe4H7hd0q2l680HPg/cXSqbtH11Sed44N81vkZmSGRP2gwmgcXAn20XZfOAV23PAxbGsukErXHgTkl7AGyvBvba3izpmVjnFMJ96zOl874A3FD6fDpQ9ryZEZE96YixfSFhOWWC4P2Kv8uBtxEG1O5Y/bwOGgvj6ynACZQGn6QXCQ+LVpZOWRxfp+N55wPvJkyLi+n1GHBPz18sMzCyJx0hto8BNgE3S3qi5di++Ha5pF/a3grcFh8w/R6YIXjNrwAGthMG+iGO9oDbgEuB6+LnfbHel2y/Qlj2uRe4yPYu4EfA0+RB2giyJx0t1wAnEgbJLCQdAF4iPjwCPkd4Svs1wrLMDsLDpsc4cq86AfxJ0n9b5LYBS2yfGrX/QVjiuQx4ANhMeJC0HHgc+CfwWUlvDOA7ZvpkXt4WmMk0m+xJM5mGkwdpJtNwFgDYznPeTKah5HvSTKbh1F6CiWtxPwXeCbwBnCGp1s6UQWgMQ2uuiOuazwF3SVo7Ko1haPXRhvcCdwAnEcLrviPprrnWGIZWv/RyTzoF3CBpGWFx/fURaQxDa664nrDUMWqNYWj1ykHg2vg7XgjcavstI9AYhlZf1JruxnW2TZI+1esFB6ExDK25Iu7muYmweeC0XjzXIDSGoTVI4qaKiyT9ZZQaw9Cqy1HT3arIf+A9wLTte+P7uyXd2HJ+t6wAS7pp1GCQWm2xvZ6wW2cpwUs/DqyXtLtN3TG6ZE0gbEhYB5zV5vzUjAodNXpgkFodSbRNUXcCeFN5QNTNNtFOo4+2D0yrRfdcwiaSCcK2zCslTbXWm99y0iqqI/8XEIKE1xBCp1bYXtGi2S0rQIpGKj1r2Z6y/a2EqucTtsmdRegkB4HfFkHWJb1VdMmaYPti4AVJL3S4VteMCgkayfSqVcN2Rf1VpGWUINr1Z8BVLTLJ2SYqNGpTV6umbRYR9mVfA/ynU6XDnjQx8n8psLP4j2J7C2Hb2rb4OSUrwF+rNGJZasaArlr9IunTLddfCfwLOJswRUzOmgCcAXzR9mWEH+gY2wckfbtGRoWOGqU2ptqvq1a/1LANto8FfgXcJOnRUnmdbBNtNeKxWpkoqrQGgaQtwJZ4ralO9crT3a6R/7Z3ACfZXkzoqOcS9n0WpGQFqNQoZQxYkZAxoFt7hsHxhBnIy6WypKwJktYT9swW3uW00oBIyqjQRaOW/bppDYgk28SQvCngIUl3tFRLzTbRUaNmv+rWnjml2MyQFPkv6aDtDcAjhHjHByT9plSla1aABI3kjAEJWsNgE2GD+2NQO2tCFakZFbrRmIwLNW1zNmEq/LTtS2LZyhgDm2qbKo26dqnSmlMKT5oc+S9pK7C1w+EiK8D3gLcCNwJ7ylkBqjR8JGPAxlLZJLBX0m2xaFbGgC7tKWtvINzTFBwLzNguP838jKTfVWjcQsh2cE4pQqRO1oTDtHlAkGS7Ko1e7FfRnrJur7ar06+203lJMLVftdXosV9Vtaes3Xe/6kbRiDqR/1WMA49K2hPjI1cDa2x/JPH8ThkDXit97jVjwI+ZHVT96zZlHTtT/FGvAC6QtLd0qCm2g+HZr1fbNcU2je1XKRSetBz5/4vWSrYXSnqttbylTtusALaLrADXdTq3RGrGgO8maM0i3vsUGfWw/SqwXzHNSBW2NxGmPp+U9HzL4abYDoZkvz5s1xTbNLJfpbIgXmiH0yL/q0jNClBF4zIG2P4hoTNcArxs+13x0LSk6QbZDhpmvwbZplF2KbC9iLCcBGFW+z6H9eT9korMHLPm3CmR/1UkZQWoQs3MGLCGcL/yIGEBvvgr33OM3HbQWPuN3DYNtQvARwnLR08SHoY5vp/1hD1HwWQyDScHfWcyDef/hXDpFXoRdNYAAAAASUVORK5CYII=",
      "text/latex": [
       "$\\displaystyle \\frac{A C R \\omega}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "              A⋅C⋅R⋅ω               \n",
       "────────────────────────────────────\n",
       " 6  6  6      4  4  4    2  2  2    \n",
       "C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(res[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "5de8a6c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2} \\left(C^{2} R^{2} \\omega^{2} + 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "        2  2  2 ⎛ 2  2  2    ⎞      \n",
       "     A⋅C ⋅R ⋅ω ⋅⎝C ⋅R ⋅ω  + 1⎠      \n",
       "────────────────────────────────────\n",
       " 6  6  6      4  4  4    2  2  2    \n",
       "C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(res[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "d393000e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C^{3} R^{3} \\omega^{3} \\left(- C^{2} R^{2} \\omega^{2} - 1\\right)}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "       3  3  3 ⎛   2  2  2    ⎞     \n",
       "    A⋅C ⋅R ⋅ω ⋅⎝- C ⋅R ⋅ω  - 1⎠     \n",
       "────────────────────────────────────\n",
       " 6  6  6      4  4  4    2  2  2    \n",
       "C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(res[4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "2a546639",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\frac{A C^{2} R^{2} \\omega^{2}}{C^{6} R^{6} \\omega^{6} + 2 C^{4} R^{4} \\omega^{4} + C^{2} R^{2} \\omega^{2} + 1}$"
      ],
      "text/plain": [
       "                2  2  2             \n",
       "             A⋅C ⋅R ⋅ω              \n",
       "────────────────────────────────────\n",
       " 6  6  6      4  4  4    2  2  2    \n",
       "C ⋅R ⋅ω  + 2⋅C ⋅R ⋅ω  + C ⋅R ⋅ω  + 1"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(res[5])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}