{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This is a short program to solve our Damped Driven Pendulum. From the book the equation\n", "we want to solve is \n", "$$ \\phi '' + 2 \\beta \\phi ' + \\omega_0^2 \\sin{\\phi} = \\omega_0^2 \\cos{\\omega t} $$\n", "To solve this in python we will convert this single second order differential equation into two \n", "coupled first order differential equations. We can do this with the substitutions of \n", "$x_0 = \\phi$ and $x_1 = \\phi '$. This leads to the two equations\n", "$$ x_0 ' = x_1$$ \n", "and \n", "$$ x_1 ' = -2 \\beta x1 - \\omega_0^2 \\sin{x_0} + \\gamma \\omega_0^2 \\cos{\\omega t}$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math\n", "import numpy as np\n", "from scipy import integrate\n", "import matplotlib.pyplot as plt\n", "\n", "omega=math.pi\n", "omega0=1.5*omega\n", "beta=omega0/4.0\n", "gamma = 0.1\n", "\n", "def eqns(x,t):\n", " x0=x[0]\n", " x1=x[1]\n", " dxdt1=-2*beta*x1 -omega0**2 * math.sin(x0) +gamma * omega0**2 * math.cos(omega*t)\n", " return [x1,dxdt1]\n", "\n", "x0=[0.0,0.0]\n", "t = np.linspace(0,30,1000)\n", "\n", "s=integrate.odeint(eqns,x0,t)\n", "\n", "plt.plot(s)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }