vuddameri · April 28, 2024 00:29
diff --git a/assignment4-problem1.ipynb b/assignment4-problem1.ipynb
 {
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/vuddameri/873c92e824f55f5fb326fb726c8da2de/assignment4-problem1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "51e3d95c",
      "metadata": {
        "id": "51e3d95c"
      },
      "source": [
        "<h1> Problem 1: Solution of ODE Using sympy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "693e71c6",
      "metadata": {
        "id": "693e71c6"
      },
      "outputs": [],
      "source": [
        "from sympy import Eq, Function, symbols, Derivative, dsolve,diff\n",
        "from sympy.abc import t\n",
        "import numpy as np\n",
        "from matplotlib import pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "60cfd2bb",
      "metadata": {
        "id": "60cfd2bb",
        "outputId": "f2c8e580-411f-45de-8b33-8fb2239099e2"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle x{\\left(t \\right)} = \\left(C_{1} \\sin{\\left(78.0000088504963 t \\right)} + C_{2} \\cos{\\left(78.0000088504963 t \\right)}\\right) e^{- 17.77635 t}$"
            ],
            "text/plain": [
              "Eq(x(t), (C1*sin(78.0000088504963*t) + C2*cos(78.0000088504963*t))*exp(-17.77635*t))"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# define the independent variable\n",
        "x = Function('x')\n",
        "#solve ODE\n",
        "odex = 100*Derivative(x(t),t,t)+3555.27*Derivative(x(t),t)+640000*x(t)\n",
        "result = dsolve(eq=odex,func=x(t))\n",
        "result"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "95dd8f34",
      "metadata": {
        "id": "95dd8f34",
        "outputId": "8f7888cc-2fa9-4e42-c871-4fee7a43eac3"
      },
      "outputs": [
        {
          "data": {
            "text/latex": [
              "$\\displaystyle x{\\left(t \\right)} = 0.0941025534249449 e^{- 17.77635 t} \\sin{\\left(78.0000088504963 t \\right)}$"
            ],
            "text/plain": [
              "Eq(x(t), 0.0941025534249449*exp(-17.77635*t)*sin(78.0000088504963*t))"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Add the initial conditions to get the constants C1 and C2\n",
        "t = symbols('t')\n",
        "x = Function('x')(t)\n",
        "ode = 100* x.diff(t,t) + 3555.27*x.diff(t) + 640000*x\n",
        "icx = {x.subs(t, 0): 0, x.diff(t).subs(t, 0): 7.34}\n",
        "result1 = dsolve(eq=ode, ics=icx,func=x)\n",
        "result1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "dc99d372",
      "metadata": {
        "id": "dc99d372",
        "outputId": "525878e1-87b9-4e01-b649-682c62450e1e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Eq(x(t), 0.0941025534249449*exp(-17.77635*t)*sin(78.0000088504963*t))\n"
          ]
        }
      ],
      "source": [
        "print(result1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5f4148b5",
      "metadata": {
        "id": "5f4148b5"
      },
      "outputs": [],
      "source": [
        "# Create a lambda function for plotting\n",
        "x = lambda t: 0.1*np.exp(-17.78*t)*np.sin(78.0*t)\n",
        "t = np.arange(0,0.5,0.005)\n",
        "xt = x(t)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "faa21d2f",
      "metadata": {
        "id": "faa21d2f",
        "outputId": "72bc826f-aa85-4bd8-b150-69521bdfb551"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Make plot\n",
        "plt.plot(t,xt,color='blue')\n",
        "plt.xlabel('t (secs))')\n",
        "plt.ylabel('x ft')\n",
        "plt.grid()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9098b537",
      "metadata": {
        "id": "9098b537"
      },
      "outputs": [],
      "source": []
    }
  ],
  "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
 }
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "view-in-github",
	"colab_type": "text"
	},
	"source": [
	"<a href=\"https://colab.research.google.com/gist/vuddameri/873c92e824f55f5fb326fb726c8da2de/assignment4-problem1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "markdown",
	"id": "51e3d95c",
	"metadata": {
	"id": "51e3d95c"
	},
	"source": [
	"<h1> Problem 1: Solution of ODE Using sympy"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"id": "693e71c6",
	"metadata": {
	"id": "693e71c6"
	},
	"outputs": [],
	"source": [
	"from sympy import Eq, Function, symbols, Derivative, dsolve,diff\n",
	"from sympy.abc import t\n",
	"import numpy as np\n",
	"from matplotlib import pyplot as plt"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"id": "60cfd2bb",
	"metadata": {
	"id": "60cfd2bb",
	"outputId": "f2c8e580-411f-45de-8b33-8fb2239099e2"
	},
	"outputs": [
	{
	"data": {
	"text/latex": [
	"$\\displaystyle x{\\left(t \\right)} = \\left(C_{1} \\sin{\\left(78.0000088504963 t \\right)} + C_{2} \\cos{\\left(78.0000088504963 t \\right)}\\right) e^{- 17.77635 t}$"
	],
	"text/plain": [
	"Eq(x(t), (C1sin(78.0000088504963t) + C2cos(78.0000088504963t))exp(-17.77635t))"
	]
	},
	"execution_count": 2,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"# define the independent variable\n",
	"x = Function('x')\n",
	"#solve ODE\n",
	"odex = 100Derivative(x(t),t,t)+3555.27Derivative(x(t),t)+640000*x(t)\n",
	"result = dsolve(eq=odex,func=x(t))\n",
	"result"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"id": "95dd8f34",
	"metadata": {
	"id": "95dd8f34",
	"outputId": "8f7888cc-2fa9-4e42-c871-4fee7a43eac3"
	},
	"outputs": [
	{
	"data": {
	"text/latex": [
	"$\\displaystyle x{\\left(t \\right)} = 0.0941025534249449 e^{- 17.77635 t} \\sin{\\left(78.0000088504963 t \\right)}$"
	],
	"text/plain": [
	"Eq(x(t), 0.0941025534249449exp(-17.77635t)sin(78.0000088504963t))"
	]
	},
	"execution_count": 3,
	"metadata": {},
	"output_type": "execute_result"
	}
	],
	"source": [
	"# Add the initial conditions to get the constants C1 and C2\n",
	"t = symbols('t')\n",
	"x = Function('x')(t)\n",
	"ode = 100* x.diff(t,t) + 3555.27x.diff(t) + 640000x\n",
	"icx = {x.subs(t, 0): 0, x.diff(t).subs(t, 0): 7.34}\n",
	"result1 = dsolve(eq=ode, ics=icx,func=x)\n",
	"result1"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"id": "dc99d372",
	"metadata": {
	"id": "dc99d372",
	"outputId": "525878e1-87b9-4e01-b649-682c62450e1e"
	},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"Eq(x(t), 0.0941025534249449exp(-17.77635t)sin(78.0000088504963t))\n"
	]
	}
	],
	"source": [
	"print(result1)"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"id": "5f4148b5",
	"metadata": {
	"id": "5f4148b5"
	},
	"outputs": [],
	"source": [
	"# Create a lambda function for plotting\n",
	"x = lambda t: 0.1np.exp(-17.78t)np.sin(78.0t)\n",
	"t = np.arange(0,0.5,0.005)\n",
	"xt = x(t)"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"id": "faa21d2f",
	"metadata": {
	"id": "faa21d2f",
	"outputId": "72bc826f-aa85-4bd8-b150-69521bdfb551"
	},
	"outputs": [
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"# Make plot\n",
	"plt.plot(t,xt,color='blue')\n",
	"plt.xlabel('t (secs))')\n",
	"plt.ylabel('x ft')\n",
	"plt.grid()\n",
	"plt.show()"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"id": "9098b537",
	"metadata": {
	"id": "9098b537"
	},
	"outputs": [],
	"source": []
	}
	],
	"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
	}
No results found