{ "cells": [ { "cell_type": "code", "execution_count": 9, "id": "southwest-opportunity", "metadata": {}, "outputs": [], "source": [ "# In this tutorial we solve first and secord order ordinary differential\n", "# equations.\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 10, "id": "loaded-emission", "metadata": {}, "outputs": [], "source": [ "# We will use 'odeint' from the 'SciPy' module. 'odeint' solve the differential\n", "# equations numerically. In this tutorial will will use differential equations\n", "# that have exact analytical solutions so that we can verify that the solutions\n", "# come out as expected.\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 11, "id": "utility-sellers", "metadata": {}, "outputs": [], "source": [ "# First, we will solve the first-order differential equation that describes\n", "# charging a capacitor C to a voltage V0 through a resistor R.\n", "R = 1e3 # ohms\n", "C = 1e-9 # Farads\n", "V0 = 1 # volts" ] }, { "cell_type": "code", "execution_count": 12, "id": "celtic-military", "metadata": {}, "outputs": [], "source": [ "# The differential equation is V0 - R*(dq/dt) - q/C = 0. To use odeint,\n", "# we must define a function that returns dq/dt. Therefore, our function\n", "# will return dq/dt = V0/R -q/(RC).\n", "def current(q,t):\n", " return V0/R - q/(R*C)" ] }, { "cell_type": "code", "execution_count": 13, "id": "integrated-discrimination", "metadata": {}, "outputs": [], "source": [ "# Here is the list of times for which we would like to know q(t).\n", "time = np.arange(0, 5e-6, 0.01e-6)" ] }, { "cell_type": "code", "execution_count": 14, "id": "temporal-seattle", "metadata": {}, "outputs": [], "source": [ "# Here is the call to odeint(). odeint returns the solution to the ode\n", "# (in our case the charge). The option between 'current' and 'time' is the\n", "# intial condition q(0), i.e. the charge at time t = 0.\n", "charge = odeint(current, 0, time) " ] }, { "cell_type": "code", "execution_count": 15, "id": "hazardous-petroleum", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Let's plot the charge as a function of time. As expected, the charge \n", "# asymptotically approaches a constant,\n", "plt.plot(time, charge, 'orange', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('charge')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 16, "id": "superior-thanksgiving", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# We can also get the current in the circuit by calling our original function.\n", "# As expected, it's an exponetial decay.\n", "plt.plot(time, current(charge, time), 'black', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('current')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 18, "id": "derived-inspection", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# If we wanted, we could plot the capacitor voltage q/C, the resistor voltage\n", "# IR and their sum.\n", "VC = charge/C\n", "VR = current(charge, time)*R\n", "plt.figure()\n", "plt.plot(time, VC, 'r', linewidth = 2, label = r'$V_C$')\n", "plt.plot(time, VR, 'b', linewidth = 2, label = r'$V_R$')\n", "plt.plot(time, VC + VR, 'k--', linewidth = 2, label = r'$V_C + V_R$')\n", "plt.xlabel('time')\n", "plt.ylabel('voltage')\n", "plt.grid(True)\n", "plt.legend();\n", "# Kirchhoff's voltage loop rule is confirmed!" ] }, { "cell_type": "code", "execution_count": 19, "id": "democratic-program", "metadata": {}, "outputs": [], "source": [ "# Solving a second-order differential equation is a little more tricky.\n", "# The example that we will consider is a series LRC circuit connected to a\n", "# battery with voltage V0 via a switch. The differential equation is:\n", "# V0 = Lq\" + Rq' +q/C. We'll use the R and C values as above. Here is\n", "# our value of L.\n", "L = 20e-3 # Henries" ] }, { "cell_type": "code", "execution_count": 20, "id": "agricultural-radiation", "metadata": {}, "outputs": [], "source": [ "# The strategy is to write the equation as a system of two first-order \n", "# equations. This is achieved by first writing z[1] = q' and z[0] = q.\n", "# In that case, or original second-order equation becomes:\n", "# V0 = L*z[1]' + R*z[1] + z[0]/C" ] }, { "cell_type": "code", "execution_count": 21, "id": "modular-organ", "metadata": {}, "outputs": [], "source": [ "# Next, we create a function that returns q' and q'' (in that order).\n", "# q' is easy because it is just q' = z[1]\n", "# q\" is z[1]', so we solve the equation above to get:\n", "# q\" = V0/L - (R/C)*z[1] -z[0]/(LC)\n", "def q_derivatives(z,t):\n", " return [z[1], (V0/L) - (R/L)*z[1] - z[0]/(L*C)]" ] }, { "cell_type": "code", "execution_count": 22, "id": "crazy-faith", "metadata": {}, "outputs": [], "source": [ "# Here is the list of desired times.\n", "time = np.arange(0, 0.2e-3, 0.001e-3)" ] }, { "cell_type": "code", "execution_count": 23, "id": "instant-archives", "metadata": {}, "outputs": [], "source": [ "# Here is the call to 'odeint()'. This time we need to pass an array\n", "# of initial conditions, the first is for q(0) and the second is for q'(0).\n", "# The .T is necessary so that we can separately unpack the solutions as\n", "# charge and current (not intuitive, in my opinion).\n", "charge, current = odeint(q_derivatives, [0, 0], time).T " ] }, { "cell_type": "code", "execution_count": 25, "id": "electrical-ground", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# A plot of the charge as a function of time.\n", "plt.plot(time, charge, 'orange', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('charge')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('UNDERDAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 27, "id": "biblical-mitchell", "metadata": {}, "outputs": [ { "data": { "image/png": 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8yRoXJG9sFld44hWXmwkp0HkaDbFMKHVjGYdno+pEYCJAz549tW/fvhEdMD8/n759+7Jw4UIAOnXqRDhtLVmyhH/84x/UrVs3rHqhxpVsLK7wJGtckLyxWVzhiVdcbg7ZbQZO83ndAtgaYpmq6u5whuG8w3HBFn3b7NSvKo64iHZSQzIN2R0+fNjtEIwx1ZybCWkB0E5E8kSkBnAdMN2vzHTgJme23bnAPmc4rqq604FhzvNhwDtVBeG0d0BEznVm190UrE6spMKkhqKiIoYNG0Z2djZjxoxxOxxjTDXm2pCdqpaKyB3Ah0A68JKqLhORUc7+54EZwGXAauAQMLyquk7TjwLTRGQEsBG4xntMEVkP1ANqiMiVwCWquhy4FfgHUAuY6TzirronpLKyMvr06cOKFSsAeOihh+jQoQNDhw51NS5jTPXk5jkkVHUGnqTju+15n+cK3B5qXWd7EdCvkjqtK9m+EPhBqHHHyr59+wCoX79+WPWSZcjuww8/ZMWKFbRs2ZJhw4bx0EMPccsttzBgwICKGI0xJlS2UoOLvLPlwk1IydJDevHFFwG49dZb+eMf/0i/fv04fPgw//73v12NyxhTPVlCclGkPaT69euTlpbG/v37OXbsWDxCC2rHjh1Mnz6d9PR0hg0bhohUDNVNnTrVlZiMMdWbJSQXeXtI9erVC6teWlqa6yt+T506ldLSUi6//HKaNm0KwJVXXklmZiZz5sxhx44drsRljKm+LCG5KNIeErg/bPfJJ58AniTk1bBhQ/r37095eTlvvPGGK3EZY6ovS0guUdWKHlLdunXDru/mit+qWrHKxHnnnXfcvquvvhqAjz76KOFxGWOqN0tILikuLkZVyc7OJiMj/MmObq74vWHDBrZv306jRo1o3779cft++MMfAjB37lw8kySNMSY0lpBc4h2uC/f8kZebQ3bz5s0DoHfv3vjfqSMvL4/c3Fx27drF6tWrEx6bMab6soTkkkinfHu5eS2Sb0LyJyIVw3jeYT1jjAmFJSSXVOceUmXnj7y8272JyxhjQmEJySXR9pDcSkhHjx7lm2++IS0tjV69egUsYz0kY0wkLCG5JNoekltDditXrqS0tJQ2bdpQp06dgGW6d+9OZmYmS5curXifxhgTjCUkl1TXHpJ3IdVOnTpVWqZmzZp069YNVeXbb79NVGjGmGrOEpJLqus5pFASEsAZZ5wBYAnJGBMyS0guqa6z7EJNSF27dgU8d7c1xphQWEJySTTLBoH1kIwxqccSkksiXVjVq169eqSlpXHgwIGErfhdVlZGQUEBAB07dqyyrLeHtHTpUsrLy+MemzGm+rOE5JJoe0hpaWkJ7yWtX7+eo0eP0qxZs6BxN2nShNzcXA4cOMCGDRsSEp8xpnqzhOSSaHtIkPhhu1CH67zsPJIxJhyWkFwSbQ8JEj+xIdyEZOeRjDHhsITkkurYQ/IultqhQ4eQynsTkvWQjDGhsITkklj0kBKdkNatWwd4VvQOhbcn5Z0IYYwxVXE1IYnIABEpEJHVIjI6wH4Rkaed/d+KSPdgdUWkkYjMEpFVzt+GPvvuc8oXiEh/n+35zrbFzuOUeL5viP7CWEj8kN3atWuB0BOStye1cuVKm2lnjAnKtYQkIunAc8ClQGdgiIh09it2KdDOeYwEJoRQdzQwW1XbAbOd1zj7rwO6AAOA8U47XkNV9UznURjr9+urtLSUw4cPk5aWRnZ2dsTtJLKHVFZWxsaNGwFo3bp1SHUaNGhAbm4uhw8fZtOmTXGMzhiTCkJKSCIyO5RtYTobWK2qa1W1BJgCDPYrMxiYrB5fAA1EpGmQuoOBl53nLwNX+myfoqpHVXUdsNppJ+EOHjwIeHpH/je4C0ciE9KWLVs4duwYubm51K5dO+R63uuVbNjOGBNMlQlJRGqKSCOgsYg0dIbDGolIa6BZlMduDvj+s3mzsy2UMlXVzVXVbQDOX+/wW7Dj/Z8zXPeARJMlQnDo0CEguvNHkNghu3DPH3l5h+2+++67mMdkjEktGUH2/xK4C0/yWQR4f6j34xkyi0agH30NsUwodcM53lBV3SIidYE3gRuBySc0IDISz9Ahubm55OfnBzlkYLt27QIgPT094jaAimGwNWvWRNWOV3FxcaXtfPDBBwDUrl07rGNlZHi+YrNnz664LimWcbnJ4gpfssZmcYUnXnFVmZBUdRwwTkT+R1WfifGxNwOn+bxuAWwNsUyNKuruEJGmqrrNGd7zng+q9HiqusX5e0BE/oVnKO+EhKSqE4GJAD179tS+ffuG9Eb9ea/Ladq0KZG2AVTcj0hVo2rHKz8/v9J25syZA8C5554b1rEOHTrE+PHjKS4ujjjGquIKR0FBAffddx+rVq1i4MCB3HXXXeTm5kbcXqziirVkjQuSNzaLKzzxiitYDwkAVX1GRM4DWvvWUdUTfrTDsABoJyJ5wBY8Ew6u9yszHbhDRKYA5wD7nESzs4q604FhwKPO33d8tv9LRJ7E0+NrB8wXkQyggaruEpFMYCDwnyjeV1DeIbu6detG1U51GLLznkNye8huzpw59O/fv2Ldv6VLl/L222/zxRdfRD10aoyJjVAnNfwT+BtwAdDLefSM5sCqWgrcAXwIrACmqeoyERklIqOcYjOAtXgmIPwduK2quk6dR4GLRWQVcLHzGmf/NGA58AFwu6qWAVnAhyLyLbAYT4L7ezTvLZhYJaRETmqINCG1atWKrKwstm7dyoEDB+IRWlAHDhxg+PDhHDt2jCFDhvDBBx/QpUsXvvvuO4YMGUJZWZkrcRljjhdSDwlP8umsqsHO04RFVWfgSTq+2573ea7A7aHWdbYXAf0qqfMw8LDftoNAj3Bjj8bhw4eB6BNSvXr1SE9Pp7i4mJKSEmrUqBGL8AKKNCGlp6dz+umns2zZMlauXEmPHgn9qAH43//9XzZs2ED37t15+eWXyczMpH379vTq1YuZM2cyZcoUhg4dmvC4jDHHC/U6pKXAqfEM5GQSqx6SiCSkl3T06FG2bt1KWloap512WvAKftq1awd8v/RQIu3YsYMXXniBtLQ0XnrpJTIzMwFPYn3ssccA+NOf/kRpaWnCYzPGHC/UhNQYWC4iH4rIdO8jnoGlslglJEjMsN2WLVtQVZo3b17xgx4Ob0JatWpVrEML6qWXXuLYsWMMHDiQbt26Hbfvpptuok2bNqxcuZLXXnst4bEZY44XakJ6EM8Fpn8BnvB5mAhUt4TknV7eokWLiOqffvrpQOJ7SGVlZbzwwgsAjBo16oT9mZmZPPDAAwD89a9/JcYj0saYMIWUkFT1E2A9kOk8XwB8Fce4Ulp1S0ibN28GiGi4DtzrIX300Uds2LCBvLw8+vfvH7DMkCFDyMnJYcmSJXz1lX2ljXFTqLPsbgHeAF5wNjUH3o5TTCmvuiWk6tpDevPNNwG4+eabSUsL/FXPysrihhtuADzDe8YY94Q6ZHc7cD6eFRpQ1VV8vySPCVOsZtlB9eghNW/enJo1a1JYWFhxH6h4Ky8v59133wXgyiuvrLLsiBEjAHj11Vcr/tsYYxIv1IR01FnEFADnYlIbcI+Qt4cUza0nvLwXxyZzDyktLY22bdsCieslzZ8/n8LCQlq1alVxo8DKnHHGGfTo0YN9+/bx/vvvJyQ+Y8yJQk1In4jI/wK1RORi4HXg3fiFldqq25BdtD0kSPyw3fTpnkmggwcPDmlF9euuuw74fpjPGJN4oSak3wE7gSV4FlydAdwfr6BSXXUbsou2hwSJn9jgTUiDBg0KqfzVV18NwHvvvceRI0fiFpcxpnJBE5KIpAFLVPXvqnqNqv7UeW5DdhHy3g+pOiSkI0eOsHPnTtLT0zn11MivjU5kD2n79u0sW7aM2rVr06dPn5Dq5OXlcdZZZ1FcXMysWbPiHKExJpCgCUlVy4FvRKRlAuI5KVSnHtKWLVsAaNasGenp6UFKVy6RPaRPPvkEgAsuuCCs5ZS8vaRkGLbbtm0bTz31FA899BCTJk1K2GQQY9wU6pBdU2CZiMy2lRqiU1ZWVjEkFM3ty728CSleK37H4vwRJLaH5L1PS7jL4//kJz8B4P3333dtwdXy8nJGjx5Ny5YtufvuuxkzZgy33HILrVq14tlnn7WLd01KC3Vx1T/GNYqTSHFxMeC5l1Fl18aEI949pFicP/LWz8rKYseOHezfvz8mMwwrE2lC6tSpE23atGHt2rXMnz+f3r17xz64KpSUlDB06FDeeOMN0tLSuPLKK+nSpQuffPIJn332Gf/zP//DihUrePrpp6PqrRqTrEI9h/Scqn7i/0hAfCnHewuGWAzXgec26CLC/v37K+71E0ux6iH5Tv1es2ZN1HFVZvv27Xz33XfUrl2bnj3Du0OKiHD55ZcDnskNifa73/2ON954g3r16jFr1izeeust/vznP/Ppp5/y2muvUaNGDcaPH88999yT8NiMSQQ7h5RgsU5IaWlpNGzYEIC9e/fGpE1f3oTUvHnzqNtKxKrfvuePIlkIduDAgQAJvx7prbfeYuzYsWRkZPDBBx9w0UUXHbf/uuuuY+bMmWRkZPDUU0/x4osvJjQ+YxLBziElWKwTEsT34titWz13ho9FQvKeR4rnxIZ58+YBnoQUiR/96EdkZ2fzzTffVAxXxtvevXv55S9/CXgWea1sqPCiiy7i+ec9twu74447WLFiRULiMyZRQk1If8Rza+8/Yat9R8U7WyqW51DieR7Jm5CaNWsWdVuJ6CEtWLAAgLPPPjui+llZWVx88cUAzJhxwv0f4+JPf/oTO3fu5IILLuBXv/pVlWVHjBjB8OHDOXLkCDfddFNchmmNcUvIq33bOaTYiEcPKZ4Jadu2bQA0bdo06rbi3UMqLS3l66+/Bgj7/JGvRJ5HWrVqFc888wwiwtNPPx3SqhJjx46lVatWLFy4kCeffDLuMValpKSETz/9lHHjxvHII48wceJEFi5cSHl5uatxmeoppFl2InKA79euqwFkAgdVNX5TpVJUdUpIqhrThBTvHtKyZcs4fPgwbdq0qRjGjMRll10GwOzZszl8+DC1atWKVYgneOqppygtLWX48OGcddZZIdWpV68eEydOpH///jz00ENcf/31UU86CdeBAwcYO3YsY8eODfi9a9OmDbfeeiu33357XD8/k1pC7SHVVdV6zqMmcDXwbHxDS03VKSEVFRVx7NgxGjRoQO3ataNuzzv1e/v27RWfQyzNnz8fgF69ekXVTrNmzejevTuHDx9mzpw5sQgtoD179vDyyy8D8Jvf/CasupdccglXX301Bw8eDLtutD777DO6du3KmDFj2L17Nx07dmTkyJHce++9DB06lObNm7N27VruueceOnToULHqujHBRHQhjKq+DVwUrJw5UXVKSN7zR7HoHYFnRmCbNm2A+Ez99p4/ijYhQWJm27344oscOnSIH//4x3Tp0iXs+k8++SS1a9fm9ddf5z//+U8cIjzR3//+d370ox+xfv16unfvzscff8zy5ct54YUXeOyxx3jllVfYsGED7777Lt26dWPTpk0MGjSIESNGJM2tPVSV0tJSt8MwAYR6g76rfB4/FZFHsdtPRKQ6JqRYTGjwiuewXSwTku95pHisjlBWVsazz3oGGYJNZKhMy5Ytuf9+zxrHd9xxByUlJUFqROcvf/kLI0eOpLy8nHvvvZd58+Zx4YUXnnDeKz09nYEDB7Jo0SKefPJJsrKyeOmll+jTpw87duyIa4z+ysvL+fzzz7n//vu58MILadq0KRkZGWRmZlKrVi3atm3LoEGDmDZtGsuXL7eVMFwWag/pCp9Hf+AAENoyylUQkQEiUiAiq0VkdID9IiJPO/u/FZHuweqKSCMRmSUiq5y/DX323eeULxCR/j7be4jIEmff0xLKmeUIxTMhxXr5IO/5o1gmpHhNbDh8+DBLliwhLS2N7t27B68QRM+ePTnllFPYuHEjS5cujUGEx5s+fTobNmygbdu2FeesInH33XfTrl07CgoKeOqpp2IY4fH+9re/8fvf/560tLSK3lCwdQLT09P59a9/zfz588nLy2PRokWMGjWqYiWNeNq7dy+PPfYYbdu25YILLuDhhx8mPz+f7du3U15ejohw5MgR1q5dy7vvvsuECRPo0qULeXl5jB49OmGr0gdy6NAhVq5cSX5+PgsWLOCDDz5g5syZzJs3j7Vr11as9pKSVDXoA3gZaODzuiHwUih1q2gzHVgDtMEzUeIboLNfmcuAmYAA5wJfBqsLPA6Mdp6PBh5znnd2ymUBeU79dGfffKC3c5yZwKXB4u/Ro4dG4uabb1ZAJ02aFFH9QN5//30FtH///lG1M2fOnONe//nPf1ZA77333qja9TVhwgQF9Oc//3nEcQUyd+5cBbRLly5RRHe84cOHK6CPPPJIxHFV5kc/+pECOnbs2Ijb8Prwww8V0OzsbN24cWNUcQUyefJkxTMiov/4xz8iaqOoqEgvueQSBTQjI0PHjx8f0xi9jhw5oo8//rjWr1+/IuYWLVroXXfdpdOnT9f169drSUmJlpeXa3FxsS5dulT/+c9/6sUXX6xNmjSpqANo37599ZVXXtFDhw7FJVZV1dLSUv3qq6/0ySef1EGDBp0QQ2WP3Nxcveiii/TOO+/UF154QT///HPdt29f3OL0jXfDhg06ZcqUiNsAFmpleaGyHXp8Yvg6lG3hPJwE8KHP6/uA+/zKvAAM8XldgOci3Urress4z5sCBYHaBz502mkKfOezfQjwQrD4I01IV111lQI6derUiOoH8sUXXyigvXr1iqod/x+y2267LWY/ml6zZs1SQPv06RNxXIGMGzdOAb355pujiO54b7zxhgJ6/vnnRxxXIF9//bUCWrdu3Zj9iFx99dUK6DXXXBPThPTJJ59oZmamAjpu3Lio2iotLdVrr7224kd11KhRWlJSEpM4y8vLddq0aZqXl1fR/oUXXqjvv/++lpWVBa0/Z84cLSsr008//VSHDx+utWvXrminQYMGetttt+nChQu1vLw8qjhLS0t10aJF+sQTT+gVV1xxXOL0PmrUqKFt2rTRCy64QHv27Kn9+/fX/v3769lnn62tWrXSmjVrVpqo8vLy9Morr9QxY8bom2++qQUFBXr48OGQ4zty5Ihu2LBBP/vsM33llVf0oYce0hEjRmi/fv20TZs2mpGRoYAOGDAg4s+gqoQU6uKqaSLSUFX3gGdYjNAXZq1Mc8D3UvjNwDkhlGkepG6uqm4DUNVtInKKT1tfBGjrmPPcf/sJRGQkMBIgNzc3oqGHjRs3ArBu3bqYDV14l/fZsmVLVG0WFxcfV3/JkiWA59xUrGLdtWsXAMuXLw+5Tf+4AvFeM1S/fv2YxVqzZk0yMjKYN28e77zzDvXr1w87rkAef/xxAC6++GK++uqrWITKNddcw/vvv8/rr78e9Jbtodq8eTO33347x44d46qrrqJr165Rf7Y33HADbdu25a9//SvPP/88c+fO5YEHHqBx48YRt7l8+XLGjx/PsmXLAGjdujW33nprxcXR//3vf4O2UVxcXFHupptu4uqrr+bjjz/m/fffp6CggPHjxzN+/Hhat27NeeedxznnnEOXLl2CLnJ79OhR1qxZw9KlS1m8eDHffvttxf3QvE499VTOPPNMunXrRrdu3cjNza1YeLm4uJg6deocV768vJzCwkLWrVvH+vXrWbduHevWrWPDhg0Vz99+++3j6jRs2JDGjRuTnZ1NrVq1qFGjBuXl5ZSUlFBSUsLu3bvZs2dPSLc5adSoEenp6fEZeq0sU/k+gJuAFcBDeFZr+A64MZS6VbR5DTDJ5/WNwDN+Zd4HLvB5PRvoUVVdYK9fG3ucv88BN/hsfxHP9PVewH98tvcB3g0Wf6Q9pCVLluhf//pX3blzZ0T1A9m1a5cC2rBhw6ja8f+X9TnnnKOAfvrpp1G166u0tFRr1KihgB44cCCiuALp0KGDAjp//vwoIzxev379FNBXXnklorj8FRYWalZWloqIrlq1KgYRfu+RRx5RQE877TQ9cuRIVG3t2rVL27Vrp4BefvnlWlpaGpMYvZ/Zl19+qc2aNVNAGzdurG+++WbYbRUUFOiQIUMqegdNmjTR559/Xo8dOxZxXIF88803etddd2lOTs5xvZG6detqnz59dMSIEfrAAw/oo48+qmPGjNHbb79dr732Wj3jjDM0PT09YC9m+PDh+vLLL+v69esjjstfSUmJLlmyRF999VW99957dcCAAdqyZcuAMVT2SE9P12bNmmmvXr30Zz/7md577706YcIEnTlzpq5YsaJi+DKaXjjRDtl52qAzcAfwP/id64nkwUk6ZKca3X/MQEpLSxVQEYnqh8M/rpYtWyqga9asiTLC43Xq1EkBXbx4cURx+du7d68CmpmZGfUPsb+nnnpKAR0yZEjYcQXiPS83cODAGER3vKNHj1Yk5gcffDDido4cOaJ9+vRRQLt166b79++PWYy+n9n27dsrzisBOmjQIF2yZEnQNgoKCvTGG2/UtLQ0BTQrK0vvu+++qIY/Q/lvefToUZ01a5b++te/1vbt24f0A5+WlqZdunTR4cOH6+TJk3XDhg0xjyuY0tJS3bRpk3755Zc6e/Zsfeedd3TKlCn65ptv6nvvvaezZs3Sb7/9VgsLC0Ma3ow2rpgkpFg/8Az5rcUzwcA7MaGLX5nLOX5Sw/xgdYG/cvykhsed5104flLDWr6f1LDAad87qeGyYPEnU0JSVW3QoIECWlRUFHEbvnGVlZVVnDuI9UndK664QgF9/fXXw44rkNmzZyugPXv2jEF0x1u5cmXFeQT/f3mH+9+xpKSkolfw0UcfxTDK73388ceKM3Fg4cKFYdcvLy/X66+/XgFt1qyZbtq0Kabx+X9mZWVl+uyzz2rdunUr/lF1ySWX6KRJk3TJkiW6a9cuLSws1AULFui4ceO0b9++FT/2GRkZessttwTtZUQSVyi2bdumM2fO1AkTJugf/vAHveeee3TMmDE6btw4feWVV3Tu3Ll68ODBhMeVCCmXkDxxcRmwEs+Mt98720YBo5zngmeobQ2wBOhZVV1new6eob1Vzt9GPvt+75QvwGcmHdATWOrsexaQYLEnW0Jq06aNAlENA/nGVVhYWPFDHGt33323UsXstariCuTRRx9VQG+99dYYRHci77+G//vf/4YVl7/XXntNAe3cuXPUJ8er4p0406lTp7B7Nw888IACWqdOHf36669jHltln9mWLVv0jjvuqBjOrepRs2ZN/cUvfqHr1q2Le1xuS8W4qkpI0U5MiIqqzgBm+G173ue5AreHWtfZXgT0q6TOw8DDAbYvBH4QTuzJplGjRqxduzZmF8fG4xokr1jfzjyWF8QGcvnll7Ny5Uree+89+vTpE3E748aNA+DOO+8MaRHVSN1yyy2sWLGCFStWMGzYsIo70AbzzDPP8NBDD5GWlsbUqVM588wz4xajv2bNmvHMM8/w4IMPVqw88fXXX7Nnzx5UlRYtWnDWWWfRr18/fvKTn8T1jsPGPdHfQ9skhViv1hDrZYN8eVdrWLlyZUzai3dC8i4jNH36dG+POmzz58/niy++oGHDhtx4442xDO8ENWvW5O2336Z+/fq89dZb3H333VXGrao88cQT3HnnnQBMmDAhqot1o5GTk8OoUaN44403WLNmTcXsryVLljB58mSGDRtmySiFWUJKEfFKSPHoIXXs2BGA7777Luq2CgsL2bhxI9nZ2XTq1Cnq9gLp06cPOTk5fPfdd3z77bcRteHtHd1yyy0xWag2mPbt2zNlyhQyMzMZN24ct9xyS8C15IqLi/nFL37Bb3/7WwCee+45Ro4cGff4jAnEElKK8N5uIVbLB8VzyK558+ZkZ2ezc+fOqOP19o66d+8e9JqQSGVmZnLNNdcA8Nprr4Vdf+vWrUybNo20tDRuu+22WIdXqQEDBvD222+TlZXFiy++SLdu3XjxxRdZtWoVy5cvZ+zYsXTo0IGXXnqJWrVq8dprryU0PmP8WUJKEdVpyE5EKnpJBQUFUbUV7+E6r+uvvx7wJKRwbz73/PPPU1payk9+8hNatWoVj/Aqddlll/Hpp5/SuXNnVq1axS9+8Qvat29Ply5d+PWvf83WrVvp2bMnn3/+Odddd11CYzPGnyWkFBHrhBTPHhLEbtguUQnp/PPPp0WLFmzcuJG5c+eGXO/QoUM8/7xnnk6kq3pHq1evXnz11VdMmjSJSy65hNatW9O6dWt+9rOfMW3aNL788suQbw5oTDy5OsvOxE516iFBbBKSqlYkJO8yMfGSlpbGDTfcwKOPPsrEiRO54IILQqr34osvsnPnTnr16hVynXjIyspixIgRjBgxwrUYjAnGekgpojpNaoDYJKSNGzeyc+dOcnJyyMvLi1VolRo5ciQiwtSpUyksLAxa/tixY/ztb38D4L777ovrVG9jUoElpBQRy4RUXl7O9u3bgeTuIXl7Rz179kzIj31eXh4DBw6kpKSESZMmBS0/efJkNm7cSMeOHRk8eHDc4zOmurOElCJimZCKioo4duwYDRo0oFatWlG3F8jpp59OWloaa9eu5ejRoxG1kajzR77uuOMOAJ599lmOHDlSabni4mIeeOABAO6///6QLkw15mRn/5ekiFgmpHgP14Hn4s28vDzKysoiXrHBjYT04x//mO7du7Nt2zZef/31Sss9/vjjbNu2jV69ejFkyJCExWdMdWYJKUU0bOi5U/vu3bvDnpbsL94z7Ly8F7IuX7487Lrl5eUsWrQISGxCSktL44knngDgX//6V8Vn5WvRokU89thjADz55JPWOzImRPZ/SorIzMykXr16lJeXc+DAgajaivcMO6+uXbsCRLT6wcqVK9m/fz/NmzePe5z++vbty6BBgzhy5Ag/+9nPjhu62717N9dccw0lJSX88pe/dHVmnTHVjSWkFOIdtvPelTVSieohRZOQ3Biu8zVhwgSaNGnCZ599xlVXXcWSJUvIz8/nnHPOYd26dXTv3p2xY8e6Epsx1ZUlpBTivQ10tMvxVIce0vz58wH3ElKzZs34y1/+Qt26dZk5cyZdu3blwgsvZPXq1XTr1o233nqLmjVruhKbMdWVJaQU4k1IO3fujKqdRExqAM+q31lZWaxfv559+/aFVXfevHkAnHvuufEILSSnn34633zzDSNGjKBRo0Z06dKFu+++m3nz5tGyZUvX4jKmurKElEKaNGkCRD9kt2XLFsCzCGo8ZWRk0KVLFwCWLl0acr2DBw+yePFi0tLS4r5CQzB5eXlMmjSJoqIili5dyhNPPBG3qfLGpDpLSCnE20OKNiElqocEkQ3bLVy4kLKyMrp27UqdOnXiFZoxJsEsIaWQWAzZlZWVxX2VBl+RJCTvcF3v3r3jEpMxxh2WkFJILHpIhYWFlJWV0bhxY7KysmIVWqW8CWnx4sUh17GEZExqsoSUQmJxDsk7XBfv80dePXr0AODrr78OaQkhVbWEZEyKsoSUQmIxZOed0JCI80cADRo0oFOnThw9ejSkXlJBQQE7d+7klFNOoW3btvEP0BiTMJaQUkgshuwSOaHBy9vT8fZ8qjJ79mwALrroIrudgzEpxpWEJCKNRGSWiKxy/jaspNwAESkQkdUiMjqU+iJyn1O+QET6+2zvISJLnH1Pi/NrJiI3i8hOEVnsPH4Rz/ceT9VxyA6+v5YolIT08ccfA56EZIxJLW71kEYDs1W1HTDbeX0cEUkHngMuBToDQ0Skc1X1nf3XAV2AAcB4px2ACcBIoJ3zGOBzuKmqeqbzCH6jmyTVsGFDRITdu3dTWloaURuJHrKD73tIX3zxRZXlysrKmDNnDgD9+vWLe1zGmMRyKyENBl52nr8MXBmgzNnAalVdq6olwBSnXlX1BwNTVPWoqq4DVgNni0hToJ6qzlNVBSZXcsxqLT09PerbULjRQ+rcuTP16tVj48aNFccPZPHixezZs4fWrVvTpk2bhMVnjEmMDJeOm6uq2wBUdZuInBKgTHNgk8/rzcA5Qeo3B77wq9McOOY899/udbWI/BBYCfxaVX2PW0FERuLpZZGbm0t+fn6w9xlQcXFxxHWDyc7OpqioiBkzZtC6deuw41q5ciXgSUzxijGQ9u3bs3DhQiZMmHBC78f7eb322muAJ4ElMrbKxPO/YzSSNS5I3tgsrvDELS5VjcsD+A+wNMBjMLDXr+yeAPWvASb5vL4ReMZ5HrA+niG+G3y2vwhcDfQC/uOzvQ/wrvM8B8hyno8CPg7l/fXo0UMjNWfOnIjrBnPBBRcooJ988knYdefMmaM5OTkK6LZt2+IQXeWeeOIJBfT6668PGJeqau/evRXQqVOnJjS2ysTzv2M0kjUu1eSNzeIKTzRxAQu1kt/VuA3ZqeqPVfUHAR7vADucYTScv4UBmtgMnObzugXgHc+prH5ldTY7z09oS1WLVNV7AczfgR6RvePkEM3U75KSEoqKikhPT+eUUwJ1WuPniiuuAGDGjBkcO3bshP0bN25k3rx51KpVi8svvzyhsRljEsOtc0jTgWHO82HAOwHKLADaiUieiNTAM1lhepD604HrRCRLRPLwTF6Yr57hvQMicq4zu+4mbx1vYnMMAlbE4g26JZqp397bVjRt2jThdzlt164dHTt2ZO/evXz++ecn7PfeLnzgwIFkZ2cnNDZjTGK4lZAeBS4WkVXAxc5rRKSZiMwAUNVS4A7gQzxJYpqqLquqvrN/GrAc+AC4XVXLnDq3ApPwTHRYA8x0tt8pIstE5BvgTuDmeL3pRIhm6re3TiInNPjy9pKmT59+wr5p06YBcO211yY0JmNM4riSkJxhsn6q2s75u9vZvlVVL/MpN0NV26tqW1V9OFh9Z9/DTvkOqjrTZ/tCZ8iwrare4Yxloqr3qWoXVe2mqheq6neJ+RTiI5ohO29CSuSUb1+DBg0CYMqUKcfdFnz16tXMnz+f7OxsLr30UldiM8bEn63UkGKiSUjeITu3EtL555/PmWeeybZt25g4cWLF9kmTPJeGjRw5ktq1a7sSmzEm/iwhpZhTTz0VgB07doRd1+0hOxHhwQcfBOCRRx6huLiYOXPm8OWXX1KnTh3uu+8+V+IyxiSGW9chmTjJzc0FqLinUTjcHrIDz7Bd9+7d+eqrr+jcuXNFYv3Nb35TcX7MGJOarIeUYrw9pEgSknfIzq0eEnh6Sa+++irdunVj06ZNlJSUcPnll1vvyJiTgPWQUkzjxo1JS0ujqKiIY8eOkZmZGXJdt88heXXs2JEFCxbwz3/+k9atW5OWlpaQmwUaY9xlPaQU43tRa2FhoOuNA1PViokQbickgMzMTH7+85/bqt7GnEQsIaWgSM4jHThwgCNHjlC7dm3q168fr9CMMaZSlpBSUCTnkXxvO2E3vjPGuMESUgqKZOq3G7edMMYYX5aQUlAkQ3Zu3LrcGGN8WUJKQdEM2VkPyRjjFktIKSiShGQ9JGOM2ywhpaBIEtLmzZ4b6lpCMsa4xRJSCvKeQwpnUsOGDRsAaNWqVVxiMsaYYCwhpaBIekiWkIwxbrOElIIaNmxIZmYm+/fv59ChQ0HLHzx4kKKiIjIzMyt6V8YYk2iWkFKQiITVS/L2jk455ZSE37rcGGO87NcnRXknJ3inc1dl/fr1wPdDfcYY4wZLSCmqZcuWAGzcuDFoWW8PyYbrjDFusoSUorwJadOmTUHLWkIyxiQDS0gpynpIxpjqxhJSigonIXnPIVlCMsa4yZWEJCKNRGSWiKxy/jaspNwAESkQkdUiMjqU+iJyn1O+QET6+2x/WEQ2iUix3zGyRGSqU+dLEWkdh7eccJH0kGxSgzHGTW71kEYDs1W1HTDbeX0cEUkHngMuBToDQ0Skc1X1nf3XAV2AAcB4px2Ad4GzA8QyAtijqqcDTwGPxeQduizUhHT06FG2bdtGeno6TZo0SURoxhgTkFsJaTDwsvP8ZeDKAGXOBlar6lpVLQGmOPWqqj8YmKKqR1V1HbDaaQdV/UJVtwWJ5Q2gn6TAHepycnKoVasW+/btY9++fZWW8056aN68Oenp6ZWWM8aYeMtw6bi53uSgqttE5JQAZZoDvlPENgPnBKnfHPjCr06w+ylUHEdVS0VkH5AD7PIvKCIjgZHgOd+Sn58fpOnAiouLI64bjsaNG7Np0yb+/e9/k5eXF7DMl19+CUCjRo0SFle4LK7wJGtckLyxWVzhiVdccUtIIvIfINBJid+H2kSAbepmHVWdCEwE6Nmzp/bt2zdI04Hl5+cTad1wdOzYkU2bNpGbm1vp8RYvXgzAueeeS506dRISV7gS9XmFy+IKX7LGZnGFJ15xxS0hqeqPK9snIjtEpKnTu2kKFAYothk4zed1C2Cr87yy+lXVqYy3zmYRyQDqA7uD1KkWQjmPVFBQAECHDh0SEpMxxlTGrXNI04FhzvNhwDsByiwA2olInojUwDNZYXqQ+tOB65yZc3lAO2B+GLH8FPhYVYP1qqoFS0jGmOrErYT0KHCxiKwCLnZeIyLNRGQGeM7nAHcAHwIrgGmquqyq+s7+acBy4APgdlUtc9p+XEQ2A7VFZLOIPOi09SKQIyKrgbsJMOOvuvImJO+07kAsIRljkoUrkxpUtQjoF2D7VuAyn9czgBmh1nf2PQw8HGD7vcC9AbYfAa4JI/xqo23btgCsXLky4P4DBw6wdetWsrKyaNWqVUjXLBljTLzYSg0prHNnz2VbK1asoLy8/IT93kR1+umn25RvY4zrLCGlsJycHHJzczl48GDA3o8N1xljkoklpBTXpUsXAJYtW3bCPktIxphkYgkpxXkT0vLly0/YZwnJGJNMLCGluKp6SAsWLACga9euCY3JGGMCsYSU4rwTG/wTUmFhIWvXriU7O5szzjjDjdCMMeY4lpBSnLeH5D/Tbt68eQD06tWLjAy3ljQ0xpjvWUJKcY0aNeLUU0/l4MGDx10g601IvXv3dis0Y4w5jiWkk0CPHj0Ajlud1xKSMSbZWEI6CQwcOBCA6dM9SwEeO3asYkKDJSRjTLKwhHQS8Cakjz76iMOHDzN37lwOHz5Mu3btaNy4scvRGWOMhyWkk0CLFi3o0aMHhw4d4uOPP+Zvf/sbANdck5JL+BljqilLSCeJQYMGATBmzBjee+89atWqxV133eVuUMYY48MS0kli6NChZGdn89VXXwHwy1/+kiZNmrgclTHGfM8S0kmibdu2LF26lBtvvJHzzjuP3/3ud26HZIwxx7ErIk8irVu3ZvLkyW6HYYwxAVkPyRhjTFKwhGSMMSYpWEIyxhiTFCwhGWOMSQqWkIwxxiQFS0jGGGOSgiUkY4wxScESkjHGmKQgqup2DNWSiOwENgQtGFhjYFcMw4kViys8Flf4kjU2iys80cTVSlUDrltmCckFIrJQVXu6HYc/iys8Flf4kjU2iys88YrLhuyMMcYkBUtIxhhjkoIlJHdMdDuASlhc4bG4wpessVlc4YlLXHYOyRhjTFKwHpIxxpikYAnJGGNMUrCEFGMiMkBECkRktYiMDrBfRORpZ/+3ItI91LpxjmuoE8+3IjJXRLr57FsvIktEZLGILExwXH1FZJ9z7MUiMibUunGO6x6fmJaKSJmINHL2xeXzEpGXRKRQRJZWst+t71awuFz5boUYm1vfr2BxufH9Ok1E5ojIChFZJiK/ClAmvt8xVbVHjB5AOrAGaAPUAL4BOvuVuQyYCQhwLvBlqHXjHNd5QEPn+aXeuJzX64HGLn1efYH3Iqkbz7j8yl8BfJyAz+uHQHdgaSX7E/7dCjGuhH+3wogt4d+vUOJy6fvVFOjuPK8LrEz075f1kGLrbGC1qq5V1RJgCjDYr8xgYLJ6fAE0EJGmIdaNW1yqOldV9zgvvwBaxOjYUcUVp7qxbnsI8FqMjl0pVf0vsLuKIm58t4LG5dJ3y3vsYJ9ZZVz9zPwk6vu1TVW/cp4fAFYAzf2KxfU7ZgkptpoDm3xeb+bE/6CVlQmlbjzj8jUCz7+CvBT4SEQWicjIGMUUTly9ReQbEZkpIl3CrBvPuBCR2sAA4E2fzfH6vIJx47sVrkR9t8KR6O9XyNz6folIa+As4Eu/XXH9jmWEW8FUSQJs859XX1mZUOpGKuS2ReRCPD8aF/hsPl9Vt4rIKcAsEfnO+RdeIuL6Cs/aV8UichnwNtAuxLrxjMvrCuBzVfX91268Pq9g3PhuhSzB361QufH9CkfCv18iUgdPArxLVff77w5QJWbfMeshxdZm4DSf1y2ArSGWCaVuPONCRLoCk4DBqlrk3a6qW52/hcBbeLrnCYlLVferarHzfAaQKSKNQ6kbz7h8XIffcEocP69g3PhuhcSF71ZIXPp+hSOh3y8RycSTjF5V1X8HKBLf71isT4ydzA88Pc61QB7fn9jr4lfmco4/KTg/1LpxjqslsBo4z297NlDX5/lcYEAC4zqV7y/gPhvY6Hx2rn5eTrn6eM4DZCfi83LabE3lJ+gT/t0KMa6Ef7fCiC3h369Q4nLj++W878nA2CrKxPU7ZkN2MaSqpSJyB/AhnlknL6nqMhEZ5ex/HpiBZ6bKauAQMLyqugmMawyQA4wXEYBS9azmmwu85WzLAP6lqh8kMK6fAreKSClwGLhOPf8HuP15AfwE+EhVD/pUj9vnJSKv4ZkV1lhENgN/ADJ9Ykr4dyvEuBL+3QojtoR/v0KMCxL8/QLOB24ElojIYmfb/+L5B0VCvmO2dJAxxpikYOeQjDHGJAVLSMYYY5KCJSRjjDFJwRKSMcaYpGAJyRhjTNAFXyNss56IbBGRZ0MpbwnJmGpARBqIyG3O82Yi8obbMZmU8w88yxTF0kPAJ6EWtoRkTPXQALgNPFfqq+pP3Q3HpBoNsOCriLQVkQ+cdfM+FZGOobYnIj3wXDf1Uah17MJYY6qHR4G2zgWLq4BOqvoDEbkZuBLPxYg/AJ7Ac6X8jcBR4DJV3S0ibYHngCZ4Lmi8RVW/S/SbMNXORGCUqq4SkXOA8cBFwSqJSBqe7+KNQL9QD2YJyZjqYTTwA1U901mJ+T2ffT/AszJzTTxX0P9OVc8SkaeAm4CxRPjDYk5eziKr5wGvOytDAGQ5+64C/hSg2hZV7Y+nNz9DVTf51A3KEpIx1d8c9dy/5oCI7APedbYvAbpW9cNiTBXSgL2qeqb/DvUsvBpo8VWv3kAf57xnHaCGiBSrapV3krWEZEz1d9TnebnP63I8/49X+sNiTGVUdb+IrBORa1T1dfH8a6arqn4TQt2h3ufOsHLPYMkIbFKDMdXFATy3lQ6beu5ps05ErgEQj26xDM5Uf86Cr/OADiKyWURGAEOBESLyDbCMGN41NxDrIRlTDahqkYh87lwjsiKCJoYCE0TkfjyrSk/Bc4sAYwBQ1SGV7IpqKriq/gPPlPKgbLVvY4wxScGG7IwxxiQFS0jGGGOSgiUkY4wxScESkjHGmKRgCckYY0xSsIRkjDEmKVhCMsYYkxT+H4IG0kVAXxIyAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# A plot of the ccurrent as a function of time.\n", "plt.plot(time, current, 'black', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('current')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('UNDERDAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 28, "id": "serious-eugene", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# We can call our model to access dI/dt. The _, is just a place holder for\n", "# a variable that we're not going to use. That part of the model returns\n", "# I (or q'), but we already have that solution from 'odeint'.\n", "_, dIdt = q_derivatives([charge, current], time)\n", "plt.plot(time, dIdt, 'cyan', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('dI/dt')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('UNDERDAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 29, "id": "artistic-slovak", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Like we did above, we can now calculate the voltages across the various\n", "# components and their sum.\n", "VC = charge/C\n", "VR = current*R\n", "VL = dIdt*L\n", "plt.figure()\n", "plt.plot(time, VC, 'r', linewidth = 2, label = r'$V_C$')\n", "plt.plot(time, VR, 'b', linewidth = 2, label = r'$V_R$')\n", "plt.plot(time, VL, 'magenta', linewidth = 2, label = r'$V_L$')\n", "plt.plot(time, VC + VR + VL, 'k--', linewidth = 2, label = r'$V_C + V_R + V_L$')\n", "plt.xlabel('time')\n", "plt.ylabel('voltage')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('UNDERDAMPLED')\n", "plt.grid(True)\n", "plt.legend();\n", "# Kirchhoff's voltage loop rule is confirmed again! Notice, however, that is \n", "# behaviour is more complicated. The instantaneous voltage across the capacitor\n", "# can be greater than the battery voltage. Nevertheless, the loop rule is \n", "# preserved at all times (because the inductor and resistor voltages can go\n", "# negative)." ] }, { "cell_type": "code", "execution_count": 30, "id": "brutal-community", "metadata": {}, "outputs": [], "source": [ "# The LRC solution above was for an underdamped oscillator. We can easily\n", "# see the transient behaviour of an overdampled oscillator be running the same\n", "# code again after changing only a single parameter.\n", "R = 2e4 # ohms" ] }, { "cell_type": "code", "execution_count": 31, "id": "fantastic-press", "metadata": {}, "outputs": [], "source": [ "# Here is the list of desired times.\n", "time = np.arange(0, 0.15e-3, 0.0005e-3)" ] }, { "cell_type": "code", "execution_count": 32, "id": "talented-accident", "metadata": {}, "outputs": [], "source": [ "# Here we go again...\n", "charge, current = odeint(q_derivatives, [0, 0], time).T " ] }, { "cell_type": "code", "execution_count": 34, "id": "flying-melissa", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# The charge...\n", "plt.plot(time, charge, 'orange', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('charge')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('OVERDAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 35, "id": "invisible-brave", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# ... and current.\n", "plt.plot(time, current, 'black', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('current')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('OVERDAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 36, "id": "defined-ceremony", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# We can call our model to access dI/dt. The _, is just a place holder for\n", "# a variable that we're not going to use. That part of the model returns\n", "# I (or q'), but we already have that solution from 'odeint'.\n", "_, dIdt = q_derivatives([charge, current], time)\n", "plt.plot(time, dIdt, 'cyan', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('dI/dt')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('OVERDAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 37, "id": "minute-exemption", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Like we did above, we can now calculate the voltages across the various\n", "# components and their sum.\n", "VC = charge/C\n", "VR = current*R\n", "VL = dIdt*L\n", "plt.figure()\n", "plt.plot(time, VC, 'r', linewidth = 2, label = r'$V_C$')\n", "plt.plot(time, VR, 'b', linewidth = 2, label = r'$V_R$')\n", "plt.plot(time, VL, 'magenta', linewidth = 2, label = r'$V_L$')\n", "plt.plot(time, VC + VR + VL, 'k--', linewidth = 2, label = r'$V_C + V_R + V_L$')\n", "plt.xlabel('time')\n", "plt.ylabel('voltage')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('OVERDAMPLED')\n", "plt.grid(True)\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": 38, "id": "successful-colon", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The LRC circuit is critically-damped when R = 8944.27190999916 ohms.\n" ] } ], "source": [ "# Finally, we can adjust R so that we acheive the critically-damped\n", "# transient response.\n", "R = 2*np.sqrt(L/C) # ohms\n", "print('The LRC circuit is critically-damped when R =', R, 'ohms.')" ] }, { "cell_type": "code", "execution_count": 39, "id": "metallic-nutrition", "metadata": {}, "outputs": [], "source": [ "# Here is the list of desired times.\n", "time = np.arange(0, 0.05e-3, 0.001e-3)" ] }, { "cell_type": "code", "execution_count": 40, "id": "integral-lincoln", "metadata": {}, "outputs": [], "source": [ "# Here we go again...\n", "charge, current = odeint(q_derivatives, [0, 0], time).T " ] }, { "cell_type": "code", "execution_count": 41, "id": "concerned-church", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# The charge...\n", "plt.plot(time, charge, 'orange', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('charge')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('CRITICALLY-DAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 42, "id": "resistant-telephone", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# ... and current.\n", "plt.plot(time, current, 'black', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('current')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('CRITICALLY-DAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 43, "id": "indie-message", "metadata": {}, "outputs": [ { "data": { "image/png": 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KkK+nAj1xs8uAPuAz1ZecjznAGkI//5xhthURGcvM3Qd/0+w/CLdvQugNGbDs7n9d1UHMZgO/BOYBj7v75Mx7G919zwr7LAYWA3R2dnb39vZWc6id9Pf309HRMex2Fx18MDftsw+feuABTl67tq5jjRbVnnMr0TmnQedcmwULFix39/nl64e7uHtfZjk7lM3g3xZlzKwDuBL4G3f/k1l1o+G4+yXAJQDz58/3np6eag85QF9fH9Xs+0vCz5PHH3QQPQcdVNexRotqz7mV6JzToHNujOGCv/Q1cxBwJHAtIfzfQcjKIZnZeELo/8DdS0M8PGNm0919rZlNJzzytnC6s0dEUjHcXT1fBDCzm4Ej3H1zfP0F4MdD7Wuhaf8dYJW7fyXz1nXAIuCiOL+23uIbSffyi0gqqh2yYRawJfN6CzueUz6YY4APAPea2Yq47h8IgX+FmZ1DuIPyjGqLzZNa/CKSimqD/3vA7WZ2NaF//3TCHTmDcvfbGHx4+2OrrrBJ9gEmAM8BmwmPGBMRaUVV3cfv7v8H+BBhPP5NwIfc/cIc62q6Nnb8E0atfhFpZdW2+HH3O4E7c6ylcHOA+4GHgNcXXIuISF6q/uVuCg6J83sLrUJEJF8K/oyuOF9RYA0iInlT8GccHucriixCRCRnCv6MgwgDtj1CuIItItKKFPwZ44BD4/LdRRYiIpIjBX8ZdfeISKtT8JfpivO7iixCRCRHCv4yXXG+osAaRETypOAv83rCOBO/Z+DgRCIirULBX6YDmEt49u7KgmsREcmDgr+CrjhfUWANIiJ5UfBXoDt7RKSVKfgr6Ipz3dkjIq1IwV9BtsW/vcA6RETyoOCvoJPwYJbNwKPFliIi0nAK/kF0xbm6e0Sk1Sj4B6ELvCLSqhT8g+iK8xUF1iAikgcF/yC64lxdPSLSahT8gzgQmAg8CTxbcC0iIo2k4B9EG3BYXNbY/CLSShT8Q+iKc3X3iEgrUfAPQXf2iEgryi34zexSM1tnZvdl1k0xs1vMbHWc75nX8RuhK85XFFiDiEij5dni/y6wsGzd+cASd58LLImvR615QDtwP/BCwbWIiDRKbsHv7r8ENpStPhW4LC5fBpyW1/EbYQJwCGG8nvuG2VZEZKxodh9/p7uvBYjzvZt8/Jp1xfmKAmsQEWkkc/f8PtxsNnCDu8+Lrze5++TM+xvdvWI/v5ktBhYDdHZ2dvf29tZVQ39/Px0dHXXtC3DFzJn864EHcsqTT/K3q1fX/TnNNNJzHot0zmnQOddmwYIFy919/k5vuHtuEzAbuC/z+gFgelyeDjxQzed0d3d7vZYuXVr3vu7uS2IRR4/oU5prpOc8Fumc06Bzrg2wzCtkarO7eq4DFsXlRcC1TT5+zUo/4roHeKXIQkREGiTP2zn/E/gNcJCZrTGzc4CLgOPMbDVwXHw9qu0F7Ee4q2dsdPSIiAxtXF4f7O7vGeStY/M6Zl4OB54g/IL34IJrEREZKf1ytwpHxfl/F1qFiEhjKPircEKc3wjkdw+UiEhzKPircAQwFXgM+EPBtYiIjJSCvwptwPFx+cYiCxERaQAFf5VK3T03FVqFiMjIKfirVGrx9wEvFViHiMhIKfirtA9h3J4XgVuLLUVEZEQU/DUojTGtfn4RGcsU/DVQP7+ItAIFfw3+EugAVgJrCq5FRKReCv4a7AK8NS6r1S8iY5WCv0alfn4Fv4iMVQr+GpX6+W8BthVZiIhInRT8NZoDzAU2AXcUW4qISF0U/HXIDtomIjLWKPjroNs6RWQsU/DXoYdwh8/twPpiSxERqZmCvw4dwBsJY/P/vOBaRERqpeCvk4ZvEJGxSsFfp1I//83oqVwiMrYo+Ot0KDAdeAq4r+BaRERqoeCvk7Gj1X99kYWIiNRIwT8CZ8T5vwOvFFmIiEgNFPwjsBA4AHgUuKHYUkREqqbgH4E24Ly4/PUiCxERqYGCf4Q+BEwEfkEYp19EZLQrJPjNbKGZPWBmD5rZ+UXU0CivAhbF5X8pshARkSo1PfjNrB34JnAi8FrgPWb22mbX0Uil7p7vARuLLEREpArjCjjmUcCD7v4wgJn1AqcCvy+gloY4BDiOMEb/pcCnii1HpC5OeMbE1jhty8y3lb1+pcK80rS9ivn2eOztw0wOPDhrFr/OvPayZS9bzyDvVVrPCOb1LFPlNrOmTaNnkP3qVUTwzwCeyLxeA/xF+UZmthhYDNDZ2UlfX19dB+vv769731r07LUXtxx6KP/04ot0/e53tOd+xME165xHk1Y5Zwe2trXxYns7L7S382J7Oy+1tfFSezsvZ5Zfamtj8957c/kjj7ClrY2X29rYkpm2ls/N2NrWxjYztsXX2Xlp/ag3Z07RFTTdu3bdteF/tosIfquwbqcvQne/BLgEYP78+d7T01PXwfr6+qh331q8Cfg28Mhuu/F8Tw+n5H7EwTXrnEeT0XLO2wkP6XmO0O1XmjbE+Sbgj3H6U9m8P05F/iakHRgfp3EV5tmpPU7Z5aGmtjhllytNVraNZeZrHn+c2bNmYWXry6fsegbZptJ6RjCvZ5kqttn6xz82/M92EcG/Btgv83omYeSDMa2d0Nf/KcJF3iKDXxprC7AWeAZ4OjM9E6dnCUH/HGGY7pEG9y7AJMIosB2Eu8Z2z8x3B3YD1j/xBK/Zbz8mxNe7ARMy064Vpl0qTOMz02hv8/c9/DA9s2YVXUZT9W3e3PDPLCL47wDmmtn+wJPAWcB7C6ij4f4a+F+EoZp/T7hyLaPbdkKIPwo8AjxOaJmsIfzhXEMI91q8CtgLmALsWWF6VZz2yMxL00RCGFej76GH6Nlvv+E3FCnT9OB3921mdh7hAVbtwKXu3hK3wE8Gzgb+DfgGcHGh1UjJVkKwrwb+EKeHCUH/GPDyMPu3AfsQBuXrjMulqROYBkyN015UH9wiRSmixY+7/xT4aRHHztt5hOC/DPgy4ctAmuMl4H7CaKkr4/QAIeS3DbHfVGB/YDYwi9APOTMzdVLQXxSRnOjPc4O9DjgWWAJ8C/hMseW0rLXAXcCdcX77UUfxFDtu4csyQqC/Jk5zgQMJYf9qQj+6SEoU/Dn4O0LwfxE4DTio0GrGvmeB38VpOSHony7faPfdaQcOJnz5vg6YR/iNxQGEC58iEij4c7AQ+ADhl7xnA79C/6GrtQ1YAfwG+C0h7B+qsN2rgC7gCOBwYMsdd/D+I49k1+aUKTKmKY9y8nWgD7gduJBwt4/sbAuwDPjvOP2KcC971u7AkcDRwHxC2O/PwHud+55/XqEvUiUFf04mA/8BvA34EnAS0F1kQaPEdkK//C2E7rBfAy+WbXMgcAwh6I8mdNnoD6pI4+jvU46OBT5OaP1/gNA/nWJf82OEoL+F8BuHDWXvvxZ4M/CWON+3qdWJpEfBn7MLCT9YWAV8DvhKseU0xVZCl81P4rSq7P1XEwa1Ow7oAfZuZnEiouDP2+6Ei7xvAL4KvANYUGhF+XiW8MOMnwA3E8aeKZlE+NdPKewPZPDxSkQkfwr+JjgSuIBwe+cHgXsId6WMdQ8C18bpVwy8h/5g4O1xeiNhHBgRGR0U/E3yOUJreBlwJnAFYy/8nXCd4po4ZcfZGE+4kH0yIezTGzxXZOxQ8DfJeEKXzxsJXSFvAK4jdHuMZtuA24Cr45R9kMIehLuVTiP8dmGsfZGJpErB30QHE+7rP4XQWj4K+DGh/3s0eZFw9801hG6c9Zn39iUE/WmEu3A0IJnI2KPgb7I5hHvX3w9cD5wA/DNwLsVe8FwP3EAI+puAFzLvHQi8Ezid8GU12sdsF5GhKfgLsAeh2+QC4CLCiJ73Eh7g0qyLoE4YxfImQuDfysCLs92EByGfThj3RnfhiLQOBX9B2gn3+M8DziGM5Plz4MPAIsLY7422nvAjqpsI1xmyjz0bR+hyOpXQFaXHe4i0LgV/wd5HGCb43YTByD5L+JfAyYQvgYXU9z9pG+EpYLdnpnsY+HDjfQhdTQuBE9HFWZFUKPhHgaMI98TfRHhg+/XsuD9+X0JLfHpcnp5ZdgY++7W0/NuuLh5kYD89hAuxbyKE/QnAoagLRyRFCv5Rop1wa+RJhAC/nPAlsJpwG2hNJk8GwoXkozLT4YRfEotI2hT8o9A+wKeBvyeMSX8/oT9+bZxKy8aOZ8Bm55vvuYdzXv96pja/dBEZAxT8o5gRfuj1hhr369uwQaEvIoPSLdkiIolR8IuIJEbBLyKSGAW/iEhiFPwiIolR8IuIJEbBLyKSGAW/iEhizN2H36pgZvYs8Fidu08FnmtgOWOBzjkNOuc0jOScX+3u08pXjongHwkzW+bu84uuo5l0zmnQOachj3NWV4+ISGIU/CIiiUkh+C8puoAC6JzToHNOQ8PPueX7+EVEZKAUWvwiIpKh4BcRSUxLB7+ZLTSzB8zsQTM7v+h68mZml5rZOjO7r+hamsHM9jOzpWa2ysxWmtkniq4pb2Y2wcxuN7O74zl/seiamsXM2s3sLjO7oehamsHMHjWze81shZkta+hnt2ofv5m1A38AjgPWAHcA73H33xdaWI7M7M1AP3C5u88rup68mdl0YLq732lmk4DlwGkt/v/YgInu3m9m44HbgE+4+28LLi13ZvZJYD6wh7ufXHQ9eTOzR4H57t7wH6y1cov/KOBBd3/Y3bcAvcCpBdeUK3f/JbCh6Dqaxd3XuvudcXkzsAqYUWxV+fKgP74cH6fWbL1lmNlM4O3At4uupRW0cvDPAJ7IvF5Di4dCysxsNnA48LuCS8ld7PJYAawDbnH3lj9n4GvAp4HtBdfRTA7cbGbLzWxxIz+4lYPfKqxr+ZZRisysA7gS+Bt3/1PR9eTN3V9x9y5gJnCUmbV0t56ZnQysc/flRdfSZMe4+xHAicDHYlduQ7Ry8K8B9su8ngk8VVAtkpPYz30l8AN3v6roeprJ3TcBfcDCYivJ3THAKbHPuxd4q5l9v9iS8ufuT8X5OuBqQvd1Q7Ry8N8BzDWz/c1sF+As4LqCa5IGihc6vwOscvevFF1PM5jZNDObHJd3A94G3F9oUTlz98+6+0x3n034e/wLd39/wWXlyswmxhsWMLOJwPFAw+7Wa9ngd/dtwHnATYSLfle4+8piq8qXmf0n8BvgIDNbY2bnFF1Tzo4BPkBoAa6I00lFF5Wz6cBSM7uH0Li5xd2TuL0xMZ3AbWZ2N3A78BN3v7FRH96yt3OKiEhlLdviFxGRyhT8IiKJUfCLiCRGwS8ikhgFv4hIkzV6QEUzeyVzZ9uwt60r+EXKmNlkMzs3Lu9rZv9VdE3Scr5LY39496K7d8XplOE2VvCL7GwycC6EX0+6+18VW460mkoDKprZAWZ2Yxyb51YzOziv44/L64NFxrCLgAPiQGirgUPcfZ6ZfRA4DWgH5gH/BOxC+BHZy8BJ7r7BzA4AvglMA14APuLuLf3rWmmIS4CPuvtqM/sL4GLgrVXuOyGO2b8NuMjdrxlqYwW/yM7OB+a5e1cc9TP7y9h5hFFAJwAPAp9x98PN7KvA2YRRJEfyF1gSFAca/Evgx2EkEgB2je+9E/hShd2edPcT4vIsd3/KzOYAvzCze939ocGOp+AXqc3SOPb/ZjP7I3B9XH8v8Pqh/gKLDKEN2BRHXR0gDj445ACEmQHdHjazPkLjZNDgVx+/SG1ezixvz7zeTmhI/fkvcGY6pNlFytgShxN/xMzOgDAAoZkdVs2+ZranmZX+dTCVMIbVkE+hU/CL7GwzMKmeHUfyF1jSMciAiu8DzokDs62k+icGHgIsi/stJfTxDxn86uoRKePu683sV/Ee61V1fMT7gH81swsIj0bsBe5uZI0ytrn7ewZ5q+ZbPN3918Chteyj0TlFRBKjrh4RkcQo+EVEEqPgFxFJjIJfRCQxCn4RkcQo+EVEEqPgFxFJzP8HsQPmgKwh3IkAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# We can call our model to access dI/dt. The _, is just a place holder for\n", "# a variable that we're not going to use. That part of the model returns\n", "# I (or q'), but we already have that solution from 'odeint'.\n", "_, dIdt = q_derivatives([charge, current], time)\n", "plt.figure()\n", "plt.plot(time, dIdt, 'cyan', linewidth = 2)\n", "plt.xlabel('time')\n", "plt.ylabel('dI/dt')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('CRITICALLY-DAMPLED')\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 44, "id": "signal-surname", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Like we did above, we can now calculate the voltages across the various\n", "# components and their sum.\n", "VC = charge/C\n", "VR = current*R\n", "VL = dIdt*L\n", "plt.figure()\n", "plt.plot(time, VC, 'r', linewidth = 2, label = r'$V_C$')\n", "plt.plot(time, VR, 'b', linewidth = 2, label = r'$V_R$')\n", "plt.plot(time, VL, 'magenta', linewidth = 2, label = r'$V_L$')\n", "plt.plot(time, VC + VR + VL, 'k--', linewidth = 2, label = r'$V_C + V_R + V_L$')\n", "plt.xlabel('time')\n", "plt.ylabel('voltage')\n", "plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))\n", "plt.title('CRITICALLY-DAMPLED')\n", "plt.grid(True)\n", "plt.legend();" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 5 }