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@benjic
Created September 20, 2015 18:32
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"input": [
"# PHSX215N Physics w/ Calculus I Lab 216\n",
"# Acceleration Due to Gravity Lab\n",
"# Ben Campbell <benjamin.campbell@umconnect.umt.edu\n",
"# September 18 2015\n",
"#-------------------------------------------#\n",
"\n",
"#Import packages and libraries needed and give them shortcut names\n",
"from __future__ import division\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"#-------------------------------------------#\n",
"#Data Section - Create Arrays for data. Perform necessary calculations\n",
"H = np.array([1.55, 1.65, 1.75, 1.81, 2.02, 2, 1.8, 1.73, 1.65, 1.55]) #meters\n",
"T = np.array([0.545, 0.57, 0.5866, 0.6019, 0.6322, 0.633, 0.6038, 0.5841, 0.5646, 0.5506]) #seconds\n",
"\n",
"Tsquared = T**2\n",
"\n",
"#--------------------------------------------#\n",
"#Create arrays for uncertainties\n",
"errHsquared = np.array([0.02] * len(H))\n",
"\n",
"\n",
"#--------------------------------------------#\n",
"#Plotting\n",
"\n",
"#Re-assign variables as x, y, dy so that the following code may remain generic\n",
"y = H #this should be the array you want to plot on the x axis\n",
"x = 1/2 * Tsquared \n",
"dy = errHsquared #this should be your error in y array\n",
" \n",
"#Find the intercept and slope, b and m, from Python's polynomial fitting function\n",
"b,m=np.polynomial.polynomial.polyfit(x,y,1,w=dy)\n",
"\n",
"#Write the equation for the best fit line based on the slope and intercept\n",
"fit = b+m*x\n",
"\n",
"#Calculate the error in slope and intercept (you do not need to understand how these are calculated). \n",
"#def Delta(x, dy) is a function, and we will learn how to write our own at a later date. They are very useful!\n",
"def Delta(x, dy):\n",
" D = (sum(1/dy**2))*(sum(x**2/dy**2))-(sum(x/dy**2))**2\n",
" return D\n",
" \n",
"D=Delta(x, dy)\n",
" \n",
"dm = np.sqrt(1/D*sum(1/dy**2)) #error in slope\n",
"db = np.sqrt(1/D*sum(x**2/dy**2)) #error in intercept\n",
"\n",
"#Calculate the \"goodness of fit\" from the linear least squares fitting document\n",
"def LLSFD2(x,y,dy):\n",
" N = sum(((y-b-m*x)/dy)**2)\n",
" return N\n",
" \n",
"N = LLSFD2(x,y,dy)\n",
"\n",
"#Plot data on graph. Plot error bars and place values for slope, error in slope and goodness of fit on the plot using \"annotate\"\n",
"plt.figure(figsize=(15,10))\n",
" \n",
"plt.plot(x, fit, color='green', linestyle='--')\n",
"plt.scatter(x, y, color='blue', marker='o')\n",
" \n",
" \n",
"#create labels YOU NEED TO CHANGE THESE!!!\n",
"plt.xlabel('$\\\\frac{1}{2}$ t$^2$ (s$^2$)')\n",
"plt.ylabel('Height h (m)')\n",
"plt.title('Duration of Fall vs Height')\n",
" \n",
"plt.errorbar(x, y, yerr=dy, xerr=None, fmt='none') #don't need to plot x error bars\n",
" \n",
"plt.annotate('Slope (m/s$^2$) = {value:.{digits}E}'.format(value=m, digits=2),\n",
" (0.05, 0.9), xycoords='axes fraction')\n",
" \n",
"plt.annotate('Error in Slope (m/s$^2$) = {value:.{digits}E}'.format(value=dm, digits=2),\n",
" (0.05, 0.85), xycoords='axes fraction')\n",
" \n",
"plt.annotate('Goodness of fit = {value:.{digits}E}'.format(value=N, digits=2),\n",
" (0.05, 0.80), xycoords='axes fraction')\n",
"\n",
"plt.show()\n"
],
"language": "python",
"metadata": {},
"outputs": [
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cNljSzKxjNkm6yBjT0Fk1AQAAAJXdsmVS375nnwPZymTMnzGmhaRgSZvO2eUj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\nAij+AAAAACAFUPwBAAAAQAr4f84B+ztGOhayAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f3ddc4d5cd0>"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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