101 lines
2.4 KiB
Python
101 lines
2.4 KiB
Python
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# coding: utf-8
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from __future__ import unicode_literals, division
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from lab import *
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import uncertainties.umath as u
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import matplotlib.pyplot as plt
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import numpy as np
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##
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## almost free oscillation
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## θ(t) = Ae^(-γt)sin(ωt+φ)+θ0
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G = sample(0.0421, 0.0514, 0.0421, 0.0392)
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W = sample(2.6800, 2.6600, 2.6709, 2.6700)
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g = ufloat(G.mean, G.std) # damping ratio γ
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w = ufloat(W.mean, W.std) # pulsation ω
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w0 = u.sqrt(w**2-g**2) # corrected value ω0
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T = 2*np.pi/w # oscillation period
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print('ω0: {}, γ: {}, T: {}'.format(w0, g, T))
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##
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## damped oscillation
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##
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G = sample(0.2280, 0.2130, 0.2180, 0.2150)
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W = sample(2.6602, 2.6500, 2.6600, 2.6600)
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g = ufloat(G.mean, G.std) # damping ratio γ
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w = ufloat(W.mean, W.std) # pulsation ω
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w0 = u.sqrt(w**2-g**2) # corrected value ω0
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T = 2*np.pi/w # oscillation period
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print('ω0: {}, γ: {}, T: {}'.format(w0, g, T))
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##
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## even more damped
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##
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G = sample(0.6060, 0.6150, 0.6057, 0.6060)
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W = sample(2.6000, 2.6200, 2.6100, 2.5900)
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g = ufloat(G.mean, G.std) # damping ratio γ
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w = ufloat(W.mean, W.std) # pulsation ω
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w0 = u.sqrt(w**2-g**2) # corrected value ω0
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T = 2*np.pi/w # oscillation period
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print('ω0: {}, γ: {}, T: {}'.format(w0, g, T))
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##
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## Driven oscillation
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##
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V = np.array([1.8000, 1.9000, 2.0000, 2.1000, 2.2000, # generator tension (V)
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2.3000, 2.3500, 3.0000, 3.2000, 3.4000])
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A = np.array([2.3900, 2.5400, 4.0000, 3.2900, 5.4500, # oscillation amplitude (rad)
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6.2500, 4.5200, 3.7500, 2.4200, 1.8200])
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T = np.array([4.3100, 4.0600, 3.1000, 3.4000, 2.8300, # oscillation period (s)
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2.7500, 2.9800, 1.9700, 1.8300, 1.7000])
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Tf = np.array([4.3300, 4.1048, 3.0883, 3.4069, 2.8270, # rotor period (s)
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2.7229, 2.9592, 1.9721, 1.8240, 1.7210])
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w = 2*np.pi/T # disc angular velocity
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wf = 2*np.pi/Tf # rotor angular velocity
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# polynomial fit Y=aX^2+bX+c
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Y = 1/A**2
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X = w**2
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y = 1/ufloat(A.mean(), 0.08)**2 # error estimation
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a,b,c = polynomial(X, Y, 2, y.s) # polynomial coeffs
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# plot Α - ω
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x = np.linspace(1.4,3.8,250)
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f = lambda w: 1/np.sqrt(a.n*w**4 + b.n*w**2 + c.n)
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plt.xlabel('pulsazione (rad/s)')
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plt.ylabel('ampiezza (rad)')
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plt.scatter(w, A, color='#b99100')
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plt.plot(x, f(x), '#c89d00')
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plt.show()
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# find curve parameters
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M = 1/u.sqrt(a)
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w0 = (M**2 * c)**(1/4)
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g = 1/2*u.sqrt(b*M**2 + 2*w0**2)
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print '''
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M: {}
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ω0: {}
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γ: {}
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'''.format(M,w0,g)
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