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  1. # coding: utf-8
  2.  
  3. # Lab 1
  4. # Haley Partlow
  5.  
  6. # In[1]:
  7.  
  8. get_ipython().magic(u'matplotlib inline')
  9. import numpy as np
  10. from __future__ import division
  11. import matplotlib.pyplot as plt
  12.  
  13.  
  14. # First, determine the frequency of the oscillator using the equation for frequency ${f = (\frac{1}{\lambda})*(\sqrt(\frac{F_{T}}{\mu}))}$
  15.  
  16. # In[35]:
  17.  
  18. def Frequency(l,F,m,L):
  19.     f = (1/l)*(F/(m/L))**0.5
  20.     return f
  21.  
  22.  
  23. # In[48]:
  24.  
  25. Wavelength=0.7814 #m
  26. Uncertainty_wavelength=1 #mm
  27. Force=2.45 #N
  28. Uncertainty_Force=0.03 #N
  29. Mass=0.000435 #kg
  30. Uncertainty_Mass=0.000002 #kg
  31. Length=1.555 #m
  32. Uncertainty_Length=0.001 #m
  33.  
  34. frequency = Frequency(Wavelength, Force, Mass, Length)
  35. print "Frequency = ", frequency, "Hz"
  36.  
  37.  
  38. # Second, determine the uncertainty of the frequency using Rule 4 error propagation ${\delta f = f \sqrt{(- \frac{\delta \lambda}{\lambda})^2 + (\frac{1}{2}* \frac{\delta F_{T}}{F_{T}})^2 + (\frac{-1}{2}*\frac{\delta m}{m})^2 + (\frac{1}{2}*\frac{\delta L}{L})^2}}$
  39. #
  40.  
  41. # In[43]:
  42.  
  43. def Uncertainty(el,l,eF,F,em,m,eL,L):
  44.     Part1=(-el/l)**2
  45.     Part2=(0.5*(eF/F))**2
  46.     Part3=(-0.5*(em/m))**2
  47.     Part4=(0.5*(eL/L))**2
  48.     ef=(Part1 + Part2 + Part3 + Part4)**0.5
  49.     return ef
  50.  
  51.  
  52. # In[55]:
  53.  
  54. Uncertainty_frequency = Uncertainty(Uncertainty_wavelength,Wavelength,Uncertainty_Force,Force,Uncertainty_Mass,Mass,Uncertainty_Length,Length)
  55. print "deltaf = ", Uncertainty_frequency, "Hz"
  56.  
  57.  
  58. # The frequency of the oscillator is 119.77 ${\pm}$ 1.28 Hz.  
  59.  
  60. # In[ ]:
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