{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ " MAC0209 - Modelagem e Simulação \n", "\n", "Roberto M. Cesar Jr. (IME-USP)\n", "\n", "Roberto Hirata Jr. (IME-USP)\n", "***\n", " Análise dos dados de queda livre: experimento realizado em aula \n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Preâmbulo" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Acelerômetro" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/pt2pqlXAd6qa/RR1ecSajVuoHD6qjrUWiyWrN8Z8AV+dsrCei+aql6fR4+q3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\npuTiSFPZ/V6SOwnTxq8sBX0fVXWxqla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1yuev7yTz5r3uRuk0F5G/AmOAp9IrVvopTaFL56Qnx3PDW9PDBvskOv3Yn1cE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\nQcL9GublcPjOHRg9Ndxv2rI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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# analise dos dados do acelerometro nos experimentos de queda livre\n", "\n", "acelerometro = pd.read_csv(\"https://www.ime.usp.br/~cesar/courses/mac0209/quedaLivreData.csv\")\n", "\n", "acelerometro = np.array(acelerometro)\n", "\n", "x = acelerometro[:,0]\n", "y = acelerometro[:,4]\n", "\n", "fig, ax = plt.subplots()\n", "plt.plot(x,y)\n", "plt.title('Dados do acelerometro')\n", "ax.set_xlabel('Tempo (segundos)')\n", "ax.set_ylabel('Resultante (forca g)')\n", "\n", "plt.show()\n", "\n", "# zoom na queda\n", "t0 = 500\n", "tf = 800\n", "\n", "x = acelerometro[t0:tf,0]\n", "y = acelerometro[t0:tf,4]\n", "\n", "fig, ax = plt.subplots()\n", "plt.plot(x,y)\n", "plt.title('Dados do acelerometro: zoom na queda')\n", "ax.set_xlabel('Tempo (segundos)')\n", "ax.set_ylabel('Resultante (forca g)')\n", "\n", "plt.show()\n", "\n", "# zoom na queda + passagem\n", "t0 = 500\n", "tf = 4700\n", "\n", "x = acelerometro[t0:tf,0]\n", "y = acelerometro[t0:tf,4]\n", "\n", "fig, ax = plt.subplots()\n", "plt.plot(x,y)\n", "plt.title('Dados do acelerometro: zoom na queda + passagem')\n", "ax.set_xlabel('Tempo (segundos)')\n", "ax.set_ylabel('Resultante (forca g)')\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercícios" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Crie um programa em Python que analise os dados do acelerômetro e detecte automaticamente os pontos de: \n", "\n", "
    \n", "\n", "
  1. início da estabilização (repouso) \n", "
  2. início da queda livre\n", "
  3. início da fase de forte influência do atrito do ar\n", "
  4. final da queda livre\n", "
  5. início da estabilização (repouso)\n", "
  6. início da passagem do Bob Esponja na fila indiana\n", "
  7. final da passagem do Bob Esponja na fila indiana\n", "\n", "
\n", "\n", "Calcule quanto tempo demorou cada período acima.\n", "\n", "Calcule a velocidade alcançada pelo Bob Esponja no final da queda." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "colab": { "name": "movimento-1D-stateSpace.ipynb", "provenance": [], "toc_visible": true, "version": "0.3.2" }, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 0 }