benjic/ProjectileMotionPlotting_BenCampbell.ipynb

## ProjectileMotionPlotting_BenCampbell.ipynb
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PHSX 216 Projectile Motion Plotting code"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Import our numpy, matplotlib (for plotting), and math (for standard deviation)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import math"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "We are plotting y_mean vs theta.  Will need the error in y_mean, for each point we plot as well to help with our fitting."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, let's create arrays for each of our sets of y data at each theta.  "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "CHANGE THE FOLLOWING TO USE YOUR DATA"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y1 = np.array([78.75, 78.25, 77.75, 77.25, 76.25, 75.25]) #in cm\n",
      "y2 = np.array([77.50, 76.50, 75.50, 74.00, 73.25]) # in cm\n",
      "y3 = np.array([62.50, 62.50, 61.50, 61.00, 59.25]) # in cm\n",
      "y4 = np.array([69.50, 69.00, 68.00, 69.75, 68.76]) # in cm\n",
      "y5 = np.array([61.50, 62.00, 61.00, 59.50, 59.50]) # in cm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Find the mean for each of these values and divide by 100 to convert to meters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y1mean = np.average(y1)/100\n",
      "y2mean = np.average(y2)/100\n",
      "y3mean = np.average(y3)/100\n",
      "y4mean = np.average(y4)/100\n",
      "y5mean = np.average(y5)/100\n",
      "#etc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Find the error in the mean for each value.  error(y_mean) = [standard deviation/sqrt(number of samples)].  You can use the numpy standard deviation function:  np.std(value) and the numpy square root, np.sqrt(value)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate error here\n",
      "y1_err = (np.std(y1)/np.sqrt(len(y1)))\n",
      "y2_err = (np.std(y2)/np.sqrt(len(y2)))\n",
      "y3_err = (np.std(y3)/np.sqrt(len(y3)))\n",
      "y4_err = (np.std(y4)/np.sqrt(len(y4)))\n",
      "y5_err = (np.std(y5)/np.sqrt(len(y5)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we can define arrays for y_mean, error y_mean, and theta so we can plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ymean_array = np.array([y1mean, y2mean, y3mean, y4mean, y5mean])\n",
      "yerr_array = np.array([y1_err, y2_err, y3_err, y4_err, y5_err])\n",
      "theta_array = np.array([42.40, 45.00, 50.00, 39.00, 36.00])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To keep our code generic and reusable, assign values to x, y, and dy"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = theta_array\n",
      "y = ymean_array\n",
      "dy = yerr_array\n",
      "\n",
      "#size the plot\n",
      "plt.figure(figsize=(15,10))\n",
      "\n",
      "#create scatter plot\n",
      "plt.scatter(x, y, color='blue', marker='o')\n",
      "\n",
      "#create labels\n",
      "plt.xlabel('$\\\\theta$ (degrees)')\n",
      "plt.ylabel('$y_{mean}$ (m)')\n",
      "plt.title('Height on wall vs Launcher Angle')\n",
      "\n",
      "#fitting to a 2nd degree polynomial\n",
      "c,b,a=np.polynomial.polynomial.polyfit(x,y,2,w=dy)\n",
      "\n",
      "#Create fit line\n",
      "xnew = np.linspace(x.min(), x.max(), 300)\n",
      "fit = a*xnew**2 + b*xnew +c\n",
      "\n",
      "plt.scatter(xnew, fit, color='red')\n",
      "\n",
      "print \"C = \",c , \"B = \",b, \"A = \",a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "C =  -5.21027369772 B =  0.277323043463 A =  -0.00321694504365\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OUCgUAiynac4GzvsiLlsthjNy2IF4ZSW5/vrk9tvn43cHYM+EQqEQYLkMBsmttx58QZhJ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\np9kAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f9c8cb21910>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 58
    }
   ],
   "metadata": {}
  }
 ]
}