diff --git a/homework/Homework_2018_1_04_1032478036.ipynb b/homework/Homework_2018_1_04_1032478036.ipynb new file mode 100644 index 0000000..f8763e7 --- /dev/null +++ b/homework/Homework_2018_1_04_1032478036.ipynb @@ -0,0 +1,158 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "TAREA: Para el polinomio de grado 2, \n", + "\\begin{equation}\n", + "P (t) = -4.9t^2 + 14.7t\n", + "\\end{equation}\n", + "\n", + "que interpola la caída libre de 3 segundos de vuelo de lanzamiento vertical hacia arriba, grafique:\n", + "\n", + "a) P(t) \n", + "\n", + "b) P'(t)\n", + "\n", + "c) P''(t)\n", + "\n", + "Interprete fisicamente los resultados" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "from scipy.misc import derivative\n", + "import matplotlib.pyplot as plt\n", + "%pylab inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def derivate(func,x0,dx=1,n=1,args=(),order=3):\n", + " try:\n", + " nn=np.array(x0).shape[0]\n", + " except IndexError:\n", + " nn=-1\n", + " if nn>-1:\n", + " y=[]\n", + " for xx in x0:\n", + " y.append(derivative(func,xx,dx=dx,n=n, order=order))\n", + " \n", + " y=np.array(y) \n", + " else:\n", + " y=derivative(func,xx, dx=dx, n=n, order=order)\n", + " \n", + " return y" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t=np.linspace(0,3,50)\n", + "pol=lambda t: -4.9*t**2+14.7*t" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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1vqzDsUvHTMcSwq1ke1GnlCoBvAzU1lpXBfyBJ7I7h6e6eBFGjHC033kHSpc2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\n17/PofOHDCbzblLU3ebcOVi1ytF+4gl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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure( figsize = (16,4) )\n", + "\n", + "plt.subplot(1,3,1)\n", + "plt.plot(t,pol(t), color=\"blue\", linewidth=3, label=\"P(t)\")\n", + "plt.ylabel(\"Posición(m)\")\n", + "plt.xlabel(\"Tiempo(s)\")\n", + "plt.legend( loc=\"upper right\", fontsize=8 )\n", + "plt.grid()\n", + "\n", + "plt.subplot(1,3,2)\n", + "plt.plot(t, derivate(pol,t,dx=1E-5,n=1,order=3),'g:', linewidth=3, label=\"1ra derivada\")\n", + "plt.plot(t, derivate(pol,t,dx=1E-5,n=2,order=5),'r:', linewidth=3, label=\"2da derivada\")\n", + "plt.xlabel(\"Tiempo(s)\")\n", + "plt.legend( loc=\"upper right\", fontsize=8 )\n", + "plt.grid()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "La función P(t) se obtuvo como producto de la interpolación de puntos que describían el movimiento de caída libre. De esta manera, la gráfica que se muestra en azul es dicha representación e indica la posición de la partícula desde que arranca el movimiento, alcanza su altura máxima en la mitad del tiempo (1.5s) y regresa al punto de partida a los 3s.\n", + "\n", + "Por otro lado la primera derivada de P(t), representada por la línea verde, corresponde a la velocidad y su comportamiento muestra que al ser lanzamiento vertical hacia arriba, su valor inicial es distinto de cero y en este caso corresponde a $14.7 \\frac{m}{s}$; luego cuando la altura es máxima su valor es cero y después de esto los valores se vuelven negativos, indicando un cambio en la dirección del movimiento (regresa cayendo a la altura inicial), hasta volver a alcanzar los $14.7 \\frac{m}{s}$ pero en dicho sentido.\n", + "\n", + "Por último, la segunda derivada corresponde a la velocidad y permite verificar que en este tipo de movimiento la aceleración se mantiene constante pues solo actúa la gravedad y por ende su representación gráfica es una recta de pendiente cero en un valor constante igual a $g=9.8 \\frac{m}{s²}$ y con signo de acuerdo al sistema de coordenadas." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.4.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}