138 lines
3.2 KiB
Python
138 lines
3.2 KiB
Python
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# coding: utf-8
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from __future__ import division, print_function, unicode_literals
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from lab import *
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import numpy as np
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import matplotlib.pyplot as plt
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import uncertainties.umath as u
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# known constants
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D = ufloat(0.994, 0.001)
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Ma = ufloat(1.000, 0.001)
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Mb = ufloat(1.400, 0.001)
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##
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## Part 1
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##
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X = sample(0.067,0.080,0.100,0.135,0.150,0.170,0.196,0.227) # distance from 1
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T1 = [ sample(2.0899,2.0842,2.0828,2.0823) # period 1
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, sample(2.0604,2.0575,2.0574,2.0555)
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, sample(2.0203,2.0186,2.0162,2.0170)
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, sample(1.9509,1.9493,1.9485,1.9470)
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, sample(1.9283,1.9260,1.9253,1.9208)
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, sample(1.9038,1.9009,1.8994,1.9007)
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, sample(1.8748,1.8731,1.8722,1.8733)
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, sample(1.8463,1.8485,1.8458,1.8428)
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]
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T2 = [ sample(2.0196,2.0177,2.0174,2.0179) # period 2
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, sample(2.0165,2.0159,2.0155,2.0151)
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, sample(2.0073,2.0064,2.0066,2.0070)
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, sample(1.9892,1.9899,1.9901,1.9913)
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, sample(1.9880,1.9872,1.9865,1.9865)
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, sample(1.9821,1.9815,1.9808,1.9828)
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, sample(1.9747,1.9751,1.9740,1.9730)
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, sample(1.9693,1.9683,1.9678,1.9672)
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]
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t1 = [i.mean for i in T1]
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t2 = [i.mean for i in T2]
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s1 = [i.stdm for i in T1]
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s2 = [i.stdm for i in T1]
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# quadratic fit
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a1,b1,c1 = polynomial(X, t1, 2, sigma_Y=s1)
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a2,b2,c2 = polynomial(X, t2, 2, sigma_Y=s2)
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f = lambda x: a1*x**2+b1*x+c1
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g = lambda x: a2*x**2+b2*x+c2
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x = np.linspace(X.min, X.max, 100)
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# plot T1, T2 - X
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plt.figure(1)
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plt.xlabel('distanza da 1 (m)')
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plt.ylabel('periodo (s)')
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plt.xlim(0.05,0.24)
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plt.scatter(X, t1, color='#21812b')
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plt.scatter(X, t2, color='#7755ff')
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plt.plot(x, [f(i).n for i in x], color='#21812b')
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plt.plot(x, [g(i).n for i in x], color='#7755ff')
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plt.show()
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# find intersection and calculate g
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x = ((b2-b1)-(u.sqrt)((b1-b2)**2-4*(a1-a2)*(c1-c2)))/(2*(a1-a2)) # intersection
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T = f(x) # isochronic period
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g1 = D/T**2*4*np.pi**2 # acceleration due to mass
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print('''
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Kater pendulum:
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T: ({})s
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g₁: ({})m/s²
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'''.format(T, g1))
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##
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## Part 2
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## free fall - direct measure of g
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H = sample(0.300,0.400,0.500,0.550,0.650,0.750) # drop height
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T = [ sample(0.241,0.242,0.241,0.248,0.251,0.252,0.249,0.243,0.248,0.244) # time to fall
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, sample(0.285,0.285,0.284,0.284,0.284,0.282,0.284,0.282,0.281,0.281)
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, sample(0.318,0.319,0.318,0.316,0.318,0.316,0.316,0.318,0.317,0.317)
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, sample(0.336,0.333,0.333,0.332,0.340,0.330,0.330,0.332,0.335,0.330)
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, sample(0.362,0.361,0.365,0.367,0.359,0.361,0.357,0.366,0.361,0.359)
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, sample(0.385,0.387,0.390,0.385,0.393,0.386,0.386,0.392,0.394,0.387)
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]
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t = sample(i.mean for i in T)
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St = sample(i.std for i in T)
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# linear fit y=kx where y=h, k=g/2, x=t^2
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x = np.linspace(0.2, 0.4, 100)
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k = simple_linear(t**2, H, 0.02)
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f = lambda x: x**2 * k.n
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# plot H - T
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plt.figure(2)
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plt.ylabel('altezza (m)')
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plt.xlabel('tempo di caduta (s)')
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plt.scatter(t, H)
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plt.plot(x, f(x))
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plt.show()
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# calculate g
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g2 = 2*k
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# χ² test
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alpha = chi_squared_fit(t, H, f, St)
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print('''
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Free fall:
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g₂: ({})m/s²
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χ²: α={:.3f}, α>ε: {}
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'''.format(g2, alpha, alpha>epsilon))
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##
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## Part 3
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## compare g1, g2
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alpha = check_measures(g1, g2)
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g = combine_measures(g1, g2)
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print('''
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compare g₁ g₂:
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α: {:.3f}, α>ε: {}
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combine:
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g_best: ({})m/s²
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'''.format(alpha, alpha>epsilon, g))
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