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Last active April 30, 2024 04:35
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assignment4-problem10.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/vuddameri/cb9bc81b5c518a3c316de2433b26974b/assignment4-problem10.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"id": "19eea384",
"metadata": {
"id": "19eea384"
},
"source": [
"<h1> <center> <font color='Blue'> CVEN 2320: Assignment 4: Problem 10"
]
},
{
"cell_type": "markdown",
"id": "9322429c",
"metadata": {
"id": "9322429c"
},
"source": [
"<h4> Problem Statement:"
]
},
{
"cell_type": "markdown",
"id": "1d650bcc",
"metadata": {
"id": "1d650bcc"
},
"source": [
"A spring-mass system with m = 1, c=2 and k = 26 acts under the influence of an external load\n",
"F(t) = 82 cos(4t) with x(0) = 6 and x’(0) = 0. Rewrite the 2nd order ODE as a system of two first-order ODEs and solve them numerically\n",
"using RK45 Approach. Make plots."
]
},
{
"cell_type": "markdown",
"id": "ef5f6519",
"metadata": {
"id": "ef5f6519"
},
"source": [
"<h4> Governing Equation:"
]
},
{
"cell_type": "markdown",
"id": "500aaaca",
"metadata": {
"id": "500aaaca"
},
"source": [
"The $2^{nd}$-Order ODE can be written as follows:\n",
"\n",
"$ m\\frac{d^2x}{dt^2} + c \\frac{dx}{dt} + kx = F(t) $"
]
},
{
"cell_type": "markdown",
"id": "51536094",
"metadata": {
"id": "51536094"
},
"source": [
"<h4> Rewrite of Governing Equations as a system of 2 first-order ODEs:"
]
},
{
"cell_type": "markdown",
"id": "efbb2cf7",
"metadata": {
"id": "efbb2cf7"
},
"source": [
"We can rewrite the governing equation as a system of two first-order ODEs as follows:\n",
"\n",
"$ \\frac{dx}{dt} = v \\quad x(t=0) = x_o $\n",
"\n",
"\n",
"$ \\frac{dv}{dt} + \\frac{c}{m}v + \\frac{k}{m}x = \\frac{F(t)}{m} \\quad v(t=0) = \\left. \\frac{dx}{dt}\\right|_{t=0} = v_o $ \\: We can rewrite this equation as:\n",
"\n",
"$ \\frac{dv}{dt} = \\frac{F(t)}{m}- \\frac{c}{m}v - \\frac{k}{m}x \\quad v(t=0) = v_o $\n"
]
},
{
"cell_type": "markdown",
"id": "0fc1ca9a",
"metadata": {
"id": "0fc1ca9a"
},
"source": [
"<h4> Code:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "05308926",
"metadata": {
"id": "05308926"
},
"outputs": [],
"source": [
"# load libaries\n",
"import numpy as np\n",
"from scipy.integrate import solve_ivp\n",
"from matplotlib import pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "c4e8af95",
"metadata": {
"id": "c4e8af95"
},
"outputs": [],
"source": [
"# Setup the model parameters:\n",
"# Note the forcing function will be dealt within the derivative function\n",
"m = 1\n",
"c = 2\n",
"k = 26\n",
"xo = 6\n",
"vo = 0\n",
"xx = [xo,vo] # Initial conditions\n",
"Fo =82 # Amplitude of my forcing function Fo*Cos(4t)\n",
"delt = 0.01\n",
"tmin=0\n",
"tmax=100\n",
"tspan = [tmin,tmax]\n",
"teval = np.arange(tmin,tmax+delt,delt) # Note that the first term tmin is inclsive while tmax+delt is exclusive and delt is time-step"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "56c4f4df",
"metadata": {
"id": "56c4f4df"
},
"outputs": [],
"source": [
"# Write the function for the two derivatives\n",
"def d2xdt(t,x,m,c,k,Fo):\n",
" xp = x[0] # Displacement ode\n",
" vp = x[1] # velocity ode\n",
" Ft = Fo*np.cos(4*t)\n",
" dx = vp\n",
" dv = Ft/m - (c/m)*vp-(k/m)*xp\n",
" return([dx,dv])"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "907003d9",
"metadata": {
"id": "907003d9"
},
"outputs": [],
"source": [
"# Solve the ODE using solve_ivp method which has RK45 as default\n",
"sol = solve_ivp(d2xdt,y0=xx,method='RK45',t_span=tspan,t_eval=teval,\n",
" vectorized = False, args=(m,c,k,Fo))"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "278b6e0b",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "278b6e0b",
"outputId": "f54dffcf-d371-4806-fb46-c73cff01235c"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" message: The solver successfully reached the end of the integration interval.\n",
" success: True\n",
" status: 0\n",
" t: [ 0.000e+00 1.000e-02 ... 9.999e+01 1.000e+02]\n",
" y: [[ 6.000e+00 5.996e+00 ... -6.106e+00 -6.025e+00]\n",
" [ 0.000e+00 -7.325e-01 ... 7.628e+00 8.598e+00]]\n",
" sol: None\n",
" t_events: None\n",
" y_events: None\n",
" nfev: 3698\n",
" njev: 0\n",
" nlu: 0"
]
},
"metadata": {},
"execution_count": 30
}
],
"source": [
"sol"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "6611943e",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "6611943e",
"outputId": "758f097b-a5ae-4e18-acdd-a93b4d5a21fa"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(10001,)"
]
},
"metadata": {},
"execution_count": 35
}
],
"source": [
"timex = sol.t # Times of evaluation\n",
"x = sol.y[0] # Displacement at each evaluation\n",
"v = sol.y[1] # Velocity at each evaluation\n",
"x.shape"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "78bf82e3",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 472
},
"id": "78bf82e3",
"outputId": "f3581689-6f97-4aaf-df3b-40d7f1eacef2"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"# Make plots of t versus x\n",
"plt.plot(timex,x,'blue')\n",
"plt.xlabel('time (s)')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.grid()\n",
"plt.title('Displacement versus Time')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "5fb3dd32",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 472
},
"id": "5fb3dd32",
"outputId": "94a7772c-e02d-42d1-d9c4-056424ce2451"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"timex = sol.t[0:400]\n",
"xx = x[0:400]\n",
"plt.plot(timex,xx,'blue')\n",
"plt.xlabel('time (s)')\n",
"plt.ylabel('Displacement (m)')\n",
"plt.grid()\n",
"plt.title('Displacement versus Time')\n",
"plt.grid\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0a27d4e3",
"metadata": {
"id": "0a27d4e3"
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"source": [
"You can find the code at: https://gist.github.com/vuddameri/cb9bc81b5c518a3c316de2433b26974b"
],
"metadata": {
"id": "j2s89HSrNGaj"
},
"id": "j2s89HSrNGaj"
},
{
"cell_type": "markdown",
"source": [],
"metadata": {
"id": "1VuF4AVwl0i_"
},
"id": "1VuF4AVwl0i_"
}
],
"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": "3.10.12"
},
"colab": {
"provenance": [],
"include_colab_link": true
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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