Kernel: Python 3 (system-wide)
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#Changing condition within the system. #Within the system, we can change the masses of the pendulum, the intial angule of the pendulum and angular velocity the pendulum is released at. #Here, I am changing the ratio of M to m. We can see there is a strong pattern for larger ratios until when the ratios ~ 5, the general ellipses pattern disappears. When the ratio goes to ~1.5, it comes back again and stops before the ratio drops to 1.
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import numpy as np import matplotlib.pyplot as plt import math from scipy.integrate import odeint M=1 m=1 g=9.81 def Atwood(y,t,M,m,g): #theta'(t)=omega(t) #radius'(t)=Rho(t) #omega'(t)=(1/radius(t))(-g*sin(theta(t))-2(Rho(t)*omega(t)) #Rho'(t)=(1/(M+m))(m*radius(t)*(omega(t)^2)-M*g+m*g*cos(theta(t))) theta, omega, radius, Rho = y #dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)),Rho, (1/(M+m))*(m*radius*(omega^2)-M*g+m*g*(np.cos(theta)))] dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt #y0=[theta, change in theta, radius, change in radius] y0 = [np.pi/2,0 ,1 ,0] #time points t = np.linspace(0,100,1000000) #Solving the ODE sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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7%(2*np.pi)
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0.7168146928204138
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M=2 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=3 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=4 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=5 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,100000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=6 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=7 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,1] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=8 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=8.18 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Fig 13 - μ = 8.18') plt.grid() plt.show()
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M=9 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=10 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=9 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=12 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=13 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=14.72 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Fig 16 - μ = 14.73') plt.grid() plt.show()
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M=15 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=16 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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---------------------------------------------------------------------------
NameError Traceback (most recent call last)
/tmp/ipykernel_4502/3288726025.py in <module>
7 return dydt
8
----> 9 y0 = [np.pi/2 ,0 ,1 ,0]
10 t = np.linspace(0,100,1000)
11 sul = odeint(Atwood, y0, t, args=(M,m,g))
NameError: name 'np' is not defined
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M=17 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [26]:
M=18 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [48]:
M=19 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [49]:
M=20 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=21 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=22 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [52]:
M=23 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=24 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [79]:
M=25 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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M=26 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [81]:
M=27 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [6]:
M=28 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [82]:
M=29 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [7]:
M=30 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [83]:
M=31 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [8]:
M=32 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
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In [84]:
M=33 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
Out[84]:
In [27]:
M=34 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [0.1*np.pi/2 ,0 ,1 ,0] t = np.linspace(0,10,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
Out[27]:
In [10]:
M=35 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
Out[10]:
M=36 m=1 g=9.81
def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)(-g(np.sin(theta))-2*(Rhoomega)), Rho, (1/(M+m))(mradius(omega**2)-Mg+mg*(np.cos(theta)))] return dydt
y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g))
plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
In [67]:
M=37 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
Out[67]:
In [68]:
M=38 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
Out[68]:
In [69]:
M=39 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
Out[69]:
In [70]:
M=40 m=1 g=9.81 def Atwood(y,t,M,m,g): theta, omega, radius, Rho = y dydt = [omega, (1/radius)*(-g*(np.sin(theta))-2*(Rho*omega)), Rho, (1/(M+m))*(m*radius*(omega**2)-M*g+m*g*(np.cos(theta)))] return dydt y0 = [np.pi/2 ,0 ,1 ,0] t = np.linspace(0,100,1000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Periodic Trejectories') plt.grid() plt.show()
Out[70]:
In [0]: