Analysis of Preliminary Trail Data Pulled from Cavendish Balance



In [1]:

    
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
import math as m
from scipy.signal import argrelextrema as argex
plt.style.use('ggplot')



In [2]:

    
data_dir = '../data/'
trial_data = np.loadtxt(data_dir+'20171025_cavendish_new_wire_free_decay.txt', delimiter='\t')



In [3]:

    
plt.plot(trial_data[:,0], trial_data[:,1])
plt.title("Trial Data from Cavendish Balance")
plt.ylabel("Anglular Positon (mrads)")
plt.xlabel("Time (s)")









    Out[3]:





<matplotlib.text.Text at 0x10ad349e8>

The weird behavior at the beginning occured when we were making an alteration to the experimental setup itself (doing one of our many adjustments to try and zero out our $\theta_e$. We can ignore this as it is not indicative of our data and look at where it moves into a damped harmonic oscialltion.



In [4]:

    
x_data = trial_data[:,0]
y_data = trial_data[:,1]

Trying out the scipy.optimzie library to fit this to a decaying sinuisodal curve.



In [6]:

    
from scipy.optimize import curve_fit



In [7]:

    
def decay(t, a, b, w, phi, theta_0):
    return a*np.exp(-b*t)*np.cos(w*t + phi) + theta_0



In [8]:

    
popt, pcov = curve_fit(decay, x_data, y_data , p0 = (50, 1.3e-3, 3e-2, -6e-1, 0))



In [9]:

    
popt









    Out[9]:





array([  7.62496097e+01,   1.41007983e-03,   3.22579113e-01,
        -1.02008421e+00,  -1.64742121e+01])



In [21]:

    
plt.plot(x_data, y_data, 'r-', linewidth = 0.3, label = "Raw Data")
# plt.plot(x_data, decay(x_data, *popt), 'g-', label = 'Fit of a*np.exp(-b*t)*np.cos(w*t + phi) + theta_0')
plt.title("Free Oscillation Data, No Large Masses")
plt.ylabel("Angle, Not Calibrated (mrad)")
plt.xlabel("Time (s)")
plt.legend()









    Out[21]:





<matplotlib.legend.Legend at 0x118b679b0>



In [26]:

    
plt.plot(x_data[:800], y_data[:800], 'rp', linewidth = 5, label = "Raw Data")
plt.plot(x_data[:800], decay(x_data[:800], *popt), 'g-', label = 'Fit of a*np.exp(-b*t)*np.cos(w*t + phi) + theta_0')
plt.title("Free Oscillation Data, No Large Masses")
plt.ylabel("Angle, Not Calibrated (mrad)")
plt.xlabel("Time (s)")
plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)









    Out[26]:





<matplotlib.legend.Legend at 0x1190d0ba8>



In [16]:

    
round(popt[1],5)









    Out[16]:





0.00141

$$b = 1.41 \times 10 ^{-3} \frac{1}{s}$$



In [27]:

    
np.pi*1.57E11*(0.08E-3)**4/(32*52.4E-3)









    Out[27]:





1.204836755086651e-05



In [28]:

    
np.pi*1.57E11*(25E-6)**4/(32*80E-3)









    Out[28]:





7.52609324056393e-08



In [ ]: