Basic physics and Python: simple harmonic motion

Here is simple harmonic motion simulation with a spring and a bouncing ball.
Springs are a classic example of harmonic motion, on Wikipedia you can get a grasp of the basics. Among other assumption, in my simulation I’ve assumed an ideal spring and that there is no friction (and therefore the motion will not stop by itself) however, if you like, you can implement friction easily.

Here is the spring simulation

	import numpy as np
	import matplotlib.pyplot as plt
	import matplotlib.animation as animation
	import random
	fig = plt.figure(figsize=(7,7))
	ax1 = fig.add_subplot(1,1,1)
	ax2 = fig.add_subplot(2,1,1)
	ax3 = fig.add_subplot(3,1,1)
	fig.subplots_adjust(hspace=.45)
	# Spring data
	k = 100
	m = 20
	w = np.sqrt(k/m)
	phi = 2
	A = 2
	period = 2*np.pi/w
	frequency = 1/period
	print("Period:",period,"seconds",sep=" ")
	print("Frequency:",frequency,"Hz",sep=" ")
	print("k: ",k,"N/m",sep=" ")
	def fun(t):
	global w,phi,A
	return A*np.sin(w*t+phi)
	def vel(t):
	global w,phi,A
	return A*w*np.cos(w*t+phi)
	def acceleration(t):
	global w,phi,A
	return -A*w**2*np.sin(w*t+phi)
	def position(x):
	x1 = x-1
	x2 = x+1
	y1 = 1
	y2 = -1
	p1 = [x1,y2]
	p2 = [x2,y2]
	p3 = [x2,y1]
	p4 = [x1,y1]
	return [p1,p2,p3,p4]
	counter = 0
	xt = [0]
	yt = [0]
	vy = [0]
	acy = [0]
	def animate(i):
	global counter, xt,yt,A,vy,acy
	ax3.clear()
	plt.subplot(311)
	# configure X axes
	plt.xlim(-3.5,3.5)
	# configure Y axes
	plt.ylim(-2,2)
	# labels
	plt.xlabel("x")
	plt.ylabel("y")
	plt.title("Motion of an ideal spring")
	p1 = [position(fun(counter))[0][0],position(fun(counter))[0][1]]
	p2 = [position(fun(counter))[1][0],position(fun(counter))[1][1]]
	p3 = [position(fun(counter))[2][0],position(fun(counter))[2][1]]
	p4 = [position(fun(counter))[3][0],position(fun(counter))[3][1]]
	x = [p1[0],p2[0],p3[0],p4[0],p1[0]]
	y = [p1[1],p2[1],p3[1],p4[1],p1[1]]
	linex = [-4,p1[0]]
	liney = [0,0]
	plt.plot(x,y,lw=5,color="blue")
	plt.plot(linex,liney,color="red",ls=":",lw=5)
	plt.subplot(312)
	xt.append(counter)
	vy.append(vel(counter))
	plt.title("Velocity")
	plt.xlim(0,15)
	plt.ylim(-A*w-0.5,A*w+0.5)
	plt.plot(xt,vy,lw=1,color="green")
	plt.plot([0,15],[0,0],lw=0.5,color="black")
	plt.subplot(313)
	acy.append(acceleration(counter))
	plt.title("Acceleration")
	plt.xlim(0,15)
	plt.ylim(-A*w**2-0.5,A*w**2+0.5)
	plt.plot(xt,acy,lw=1,color="green")
	plt.plot([0,15],[0,0],lw=0.5,color="black")
	counter += 0.1
	ani = animation.FuncAnimation(fig,animate,interval=2)
	plt.show()

view raw harmonicMotion1.py hosted with ❤ by GitHub

Below is the bouncing ball:

	import numpy as np
	import matplotlib.pyplot as plt
	import matplotlib.animation as animation
	import random
	fig = plt.figure()
	ax1 = fig.add_subplot(1,1,1)
	def fun(x):
	return 2*np.sin(2*x+2)
	counter = 1
	def animate(i):
	global x,y,counter
	counter += 0.2
	ax1.clear()
	plt.xlim(0,50)
	plt.ylim(-3,3)
	plt.plot([x for x in range(50)],[-2.15 for x in range(50)],lw=2,color="black")
	plt.plot(counter,fun(counter),marker="o",ms=20)
	ani = animation.FuncAnimation(fig,animate,interval=1)
	plt.show()

view raw harmonicMotion2.py hosted with ❤ by GitHub

A simpler example of simple harmonic motion with a spring (video):

	import numpy as np
	import matplotlib.pyplot as plt
	import matplotlib.animation as animation
	import random
	fig = plt.figure()
	ax1 = fig.add_subplot(1,1,1)
	def fun(t):
	return 2*np.sin(4/3*t+2)
	x = [0]
	y = [fun(x[0])]
	def position(x):
	x1 = x-1
	x2 = x+1
	y1 = 1
	y2 = -1
	p1 = [x1,y2]
	p2 = [x2,y2]
	p3 = [x2,y1]
	p4 = [x1,y1]
	return [p1,p2,p3,p4]
	counter = 0
	def animate(i):
	global x,y,counter
	ax1.clear()
	# configure X axes
	plt.xlim(-5,5)
	plt.xticks([-4,-3,-2,-1,0,1,2,3,4])
	# configure Y axes
	plt.ylim(-5,5)
	# labels
	plt.xlabel("x")
	plt.ylabel("y")
	plt.title("Simple harmonic motion")
	# plt.gca().add_line(line)
	p1 = [position(fun(counter))[0][0],position(fun(counter))[0][1]]
	p2 = [position(fun(counter))[1][0],position(fun(counter))[1][1]]
	p3 = [position(fun(counter))[2][0],position(fun(counter))[2][1]]
	p4 = [position(fun(counter))[3][0],position(fun(counter))[3][1]]
	x = [p1[0],p2[0],p3[0],p4[0],p1[0]]
	y = [p1[1],p2[1],p3[1],p4[1],p1[1]]
	linex = [-4,p1[0]]
	liney = [0,0]
	plt.plot(x,y,lw=5,color="blue")
	plt.plot(linex,liney,color="red",ls=":",lw=5)
	counter += 0.2
	ani = animation.FuncAnimation(fig,animate,interval=1)
	plt.show()

view raw harmonicMotion3.py hosted with ❤ by GitHub

Hope this was interesting.