问单摆问题的数值解

EN

#Import needed modules
import numpy as np
import matplotlib.pyplot as plt

#Initialize variables (Initial conditions)
g = 9.8 #Gravitational Acceleration
L = 2.0 #Length of the Pendulum
A0 = 3.0 #Initial amplitude of the driving acceleration
v0 = 0.0 #Initial velocity
theta0 = 90*np.pi/180 #Initial Angle
drivingPeriod = 20.0 #Driving Period


#Setting time array for graph visualization
tau = 0.1 #Time Step
tStop = 10.0 #Maximum time for graph visualization derived from Kinematics
t = np.arange(0., tStop+tau, tau) #Array of time
theta = np.zeros(len(t))
v = np.zeros(len(t))


#Verlet Method
theta[0] = theta0
v[0] = v0
for i in range(len(t)-1):
    accel = -((g + (A0*np.sin((2*np.pi*t) / drivingPeriod)))/L) * np.sin(theta[i])
    theta[i+1] = theta[i] + tau*v[i] + 0.5*tau**2*accel[i]
    v[i+1] = v[i] + 0.5*tau*(accel[i] + accel[i+1])


#Plotting and saving the resulting graph
fig, ax1 = plt.subplots(figsize=(7.5,4.5))
ax1.plot(t,theta*(180/np.pi))
ax1.set_xlabel("Time (t)")
ax1.set_ylabel("Theta")

plt.show()