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@author: yacine.mezemate
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from scipy.integrate import odeint
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import matplotlib.pyplot as plt
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x0 = np.array([theta0, omega0])
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t = np.linspace(0,pi*2,100)
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global k, damping_force
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def SystemEquation((x1,x2), t0):
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return [x2, -k*sin(x1) -damping_force*x1]
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x_t = odeint(SystemEquation, x0, t)
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plt.ylabel(r"$\theta$", fontsize=18)
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plt.xlabel(r"time", fontsize=18)
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plt.plot(x_t[:,1], x_t[:,0])
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plt.ylabel(r"$\dot{\theta}$", fontsize=18)38
plt.xlabel(r"$\theta$", fontsize=18)
"""
@author: yacine.mezemate
"""
import numpy as np
from math import *
from scipy.integrate import odeint
import matplotlib.pyplot as plt
g = 9.81
L = 1
theta0 = (10*2*pi)/360
omega0 = 5*2*pi/360
x0 = np.array([theta0, omega0])
t = np.linspace(0,pi*2,100)
global k, damping_force
damping_force = 0
k = g*L
def SystemEquation((x1,x2), t0):
return [x2, -k*sin(x1) -damping_force*x1]
x_t = odeint(SystemEquation, x0, t)
plt.figure(1)
plt.plot(t,x_t[:,0])
plt.ylabel(r"$\theta$", fontsize=18)
plt.xlabel(r"time", fontsize=18)
plt.show()
plt.figure(2)
plt.plot(x_t[:,1], x_t[:,0])
plt.ylabel(r"$\dot{\theta}$", fontsize=18)
plt.xlabel(r"$\theta$", fontsize=18)
plt.show()
, and the distance traveled along the tangent to the arc is denoted,
is the length of the pendulum.
and represent the corresponding phase space.
