Rodney Dunning's Home Page | Research and Scholarship | VPython | Simple Harmonic Motion
Introduction
Simple harmonic motion results whenever the restoring force is proportional to the displacement of the object.
Description
Description goes here.
Screen Shot
The bob executes simple harmonic motion.
Suggested Use
Suggested uses go here.
Hints:- Click anywhere in the animation scene to pause the animation. Click again to restart the animation.
Source Code
The source code appears between the bars below. Copy and paste the code into the Python IDLE environment, and hit F5 to run the code.
from visual import *
from __future__ import division
"""
Rodney Dunning
Assistant Professor of Physics
Longwood University
Simple Harmonic Motion
"""
#------------------------------------------------
# dynamical variables
#------------------------------------------------
# SI units
k = 10
A = 100
m = 1
#--------------------------------------------------
# Scene attributes and functions
#--------------------------------------------------
scene.title = "Simple Harmonic Motion"
scene.x = 0
scene.y = 0
scene.width = 600
scene.height = 600
scene.range = (1.5*A,1.5*A,1.5*A)
scene.autoscale = 0 ##0 means autoscaling is OFF
scene.userzoom = 0 ##0 means user cannot zoom
scene.userspin = 0 ##0 means user cannot spin
scene.lights = [vector(0,0,1)]
scene.ambient = 0.5
scene.label = label(visible=1,
pos=(0,0,0),
xoffset = 0,
yoffset = 0,
text = "Click to begin")
scene.mouse_label = label(visible=1,
pos=(0,A,0),
text=("Mouse position"))
def return_mouse_pos(scene):
scene.mouse_label.text = ("mouse\n x: %3.2f y: %3.2f"
%(scene.mouse.pos.x, scene.mouse.pos.y))
def check_for_pause(scene): #checks for pause request
if scene.mouse.clicked:
scene.mouse.getclick()
pause(scene)
def pause(scene):
while 1:
return_mouse_pos(scene)
if scene.mouse.clicked:
scene.mouse.getclick()
break
#---------------------------------------------------
# Variables for keeping up with the elapsed time.
#---------------------------------------------------
t = 0 # elapsed time
t_max = 1000 # seconds
dt = 0.01 # seconds
dt_2 = dt /2 # for the Verlet integrator in the main loop
#----------------------------------------------------
# The spring and the bob.
#----------------------------------------------------
spring = helix(pos = vector(-A,0,0),
length = 2*A,
coils = 25,
radius = A/10)
spring.constant = k
bob = sphere(pos = vector(A,0,0),
vel = vector(0,0,0),
acc = (-1 * spring.constant / m) * vector(A,0,0),
mass = m,
radius = A/10)
#----------------------------------------------------
# Create reference marks--as many as needed
#----------------------------------------------------
def create_reference_marks(num_marks,range_start,step,mark_list,mark_labels):
height = 0.1*A
length = 0.1*height
width = 0.1*height
for i in range(num_marks+1):
ref_mark = box()
ref_mark.color = color.white
ref_mark.height = height
ref_mark.length = length
ref_mark.width = width
ref_mark.pos = vector(range_start + step*i,0,0)
ref_mark_label = label(opacity = 0)
ref_mark_label.pos = vector(range_start + step*i,10 + ref_mark.height/2,0)
ref_mark_label.box = 0
ref_mark_label.text = "%1i" %(range_start+i*step)
mark_list.append(ref_mark)
mark_labels.append(ref_mark_label)
#----------------------------------------------------
# Create bars to illustrate the energy distribution
#----------------------------------------------------
total_energy_bar = box()
total_energy_bar.color = color.red
total_energy_bar.height = 0
total_energy_bar.length = 5
total_energy_bar.width = 5
total_energy_bar.pos = (0.75*A,-0.5*A,0)
total_energy_label = label(opacity = 0)
total_energy_label.pos = vector(0.75*A,-1.1*A,0)
total_energy_label.line = 0
total_energy_label.text = "E"
potential_energy_bar = box()
potential_energy_bar.color = color.white
potential_energy_bar.height = 0
potential_energy_bar.length = 5
potential_energy_bar.width = 5
potential_energy_bar.pos = (A,-0.5*A,0)
potential_energy_label = label(opacity = 0)
potential_energy_label.pos = vector(A,-1.1*A,0)
potential_energy_label.line = 0
potential_energy_label.text = "U"
kinetic_energy_bar = box()
kinetic_energy_bar.color = color.green
kinetic_energy_bar.height = 0
kinetic_energy_bar.length = 5
kinetic_energy_bar.width = 5
kinetic_energy_bar.pos = (1.25*A,-0.5*A,0)
kinetic_energy_label = label(opacity = 0)
kinetic_energy_label.pos = vector(1.25*A,-1.1*A,0)
kinetic_energy_label.line = 0
kinetic_energy_label.text = "K"
#--------------------------------------------------------
# Main loop
#--------------------------------------------------------
ready = 0
while not ready:
ready = scene.mouse.getclick()
scene.label.visible = 0
scene.label.text = "Finished."
num_marks = int(A/10)
reference_marks = []
reference_labels = []
create_reference_marks(num_marks, # number of marks
-A, # where the range starts
(2*A/num_marks), # step size
reference_marks,
reference_labels)
E = 0.5 * k * A**2 # total energy
potential_energy_bar.height = (0.5*k*mag(bob.pos)**2)/E
potential_energy_bar.pos.y = -0.5*A
total_energy_bar.height = potential_energy_bar.height + kinetic_energy_bar.height
total_energy_bar.pos.y = -0.5*A
while t < t_max:
rate(50)
check_for_pause(scene)
return_mouse_pos(scene)
t += dt
bob.pos += bob.vel * dt_2
spring.length = mag(bob.pos - spring.pos)
bob.acc = (-spring.constant / bob.mass) * bob.pos
bob.vel += bob.acc * dt
bob.pos += bob.vel * dt_2
spring.length = mag(bob.pos - spring.pos)
U_s = 0.5*k*mag(bob.pos)**2
potential_energy_bar.height = 0.75*A*(U_s / E)
potential_energy_bar.pos.y = -A + potential_energy_bar.height/2
K = 0.5*bob.mass*mag(bob.vel)**2
kinetic_energy_bar.height = 0.75*A*(K / E)
kinetic_energy_bar.pos.y = -A + kinetic_energy_bar.height/2
total_energy_bar.height = potential_energy_bar.height + kinetic_energy_bar.height
total_energy_bar.pos.y = -A + total_energy_bar.height/2
scene.label.visible = 1