Kernel: Python 3 (system-wide)
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import numpy as np import matplotlib.pyplot as plt import math from scipy.integrate import odeint 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(0,100,10000000) 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 5.4 - Phase Plot') plt.grid() plt.show()
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import numpy as np import matplotlib.pyplot as plt import math from scipy.integrate import odeint 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 = [(1.1*np.pi)/2 ,0 ,1 ,0] t = np.linspace(0,100,10000000) 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 5.6 - Phase Plot') plt.grid() plt.show()
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import numpy as np import matplotlib.pyplot as plt import math from scipy.integrate import odeint M=9 m=1 g=9.81 def x(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 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 x0 = [np.pi/2 ,0 ,1 ,0] y0 = [(1.1*np.pi)/2 ,0 ,1 ,0] t = np.linspace(0,100,10000000) sul = odeint(Atwood, y0, t, args=(M,m,g)) sul2 = odeint(x, x0, t, args=(M,m,g)) plt.plot(sul[:,0], sul[:,1], 'g') plt.plot(sul2[:,0], sul2[:,1], 'r') plt.ylabel('Angular velocity') plt.xlabel('Angular displacement') plt.title('Fig 5.6 - Phase Plot') plt.grid() plt.show()
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