assignmet13_Harmonic Motion-short.ipynb

Kernel: SageMath (stable)

import numpy as np
from numpy import sin, cos
from scipy.integrate import odeint
from matplotlib import pyplot as plt 


# define the equations
def equations(y0, t):
    theta, x = y0
    f = [x, -(g/l) * sin(theta)]
    return f

def plot_results(time, theta1, theta2):
    plt.plot(time, theta1[:,0])
    plt.plot(time, theta2)
    s = '(Initial Angle = ' + str(initial_angle) + ' degrees)'
    plt.title('Metotalet: ' + s)
    plt.xlabel('time (s)')
    plt.ylabel('angle (rad)')
    plt.grid(True)
    plt.legend(['nonlinear', 'linear'])
    plt.show()

# parameters
g = 9.81
l = 1.0
E_lst=[]
E=0
m=10
time = np.arange(0, 12.0, 0.025)
#def enegry(thethadot, theta):
#    E=1/2*m*l**2*thetadot+m*g*l*(1-cos(theta))
#    E_lst.append(E)
# initial conditions
initial_angle = input("choose an initial angle")
theta0 = np.radians(initial_angle)
x0 = np.radians(0.0)

# find the solution to the nonlinear problem
theta1 = odeint(equations, [theta0, x0],  time)

# find the solution to the linear problem
w = np.sqrt(g/l)
theta2 = [theta0 * cos(w*t) for t in time]
#E_lst=[1/2*m*l**2*thetadot+m*g*l*(1-cos(theta))]

# plot the results
plot_results(time, theta1, theta2)

choose an initial angle