# All lines like this one that begin with "#" are comments.
# All other lines are program statements.
# The next line is an internal revision control id:
# $Date: 2007/11/08 17:19:19 $ $Revision: 1.2 $
# Copyright (c) 2007 David M. Harrison
# Import the visual library.
from visual import *
# These four lines control the size of the window of
# the animation and the scale. The details of these lines
# are not important for our purposes.
scene.autoscale = 0
scene.height = 400
scene.width = 800
scene.range = vector(60, 60, 60)
# Create the green ball that will execute simple harmonic motion
# by numerical integration.
greenBall = sphere (color = color.green, radius = 2)
# yellowBall will execute simple harmonic motion using a sine function.
yellowBall = sphere (color = color.yellow, radius = 2)
# The initial x position of the balls: this is
# the equilibrium position.
x = 0
# Position the balls. pos is a built-in of VPython, and
# lists the (x,y,z) coordinates. The x axis is horizontal,
# y axis is vertical, and the z axis is perpendicular to
# the plane of the screen. We place the green ball just
# below the center of the scene, at y - -10.
#
greenBall.pos = (x,-10,0)
# yellowBall is above the first ball: it's y coordinate is 10,
# just above the center of the scene.
yellowBall.pos = (x, 10, 0)
# The initial x component of the velocity of the balls:
# all other components are zero.
vx = 150
# The spring constant
k = 9.0
# The mass of the balls
mass = 1.0
# The amplitude of yellowBall's motion
ampl = sqrt(mass/k) * vx
# The time
t = 0
# This is the time step
dt = 0.005
# This causes the following indented lines
# to be executed forever in a loop.
while 1 == 1:
# Set the rate of the animation
rate(1/dt)
# The acceleration in the x direction.
a = -(k/mass) * x
# Update the speed using the acceleration. Note
# that we "recycle" the variable vx, replacing the
# old value with the new one.
vx = vx + a*dt
# Update the x position of the ball using the speed.
x = x + vx*dt
# Position greenBall at the new x position
greenBall.pos = (x, -10, 0)
# Update the time
t = t + dt
# Now we calculate simple harmonic motion using
# a sine function and position yellowBall using the result
# of the calculation
x2 = ampl * sin( sqrt(k/mass)* t)
yellowBall.pos = (x2,10,0)
