SHM_demo_sincos.html

Simple Harmonic Motion
An animated demonstration

G. Fleischer for MAT-NYA (Calculus I), A2005

Instructions

To run this demonstration in Maple (9.5 or 10):
1. Go to the Edit menu and select Execute|Worksheet. This will expand both sections below.
2. Collapse Section 1 (entitled "Code for Harmonic Motion Demo Program"), by clicking on the minus sign [-], to unclutter the screen.
3. At this point only Section 2 should be open (expanded). If necessary scroll down to the animation graphic. Click on the graphic once, then
run the animation with the DVD-like buttons on the top menu bar.
4. The graph preceding the animation is a static image of the curve y = x(t).
5. Experiment with your choices of the parameters a, b, as described in Section 2. below.
6. Enjoy!

Available upon request. It is part of the Maple worksheet.

2. Demonstration of Harmonic Motion

The "arguments" in the first red line below correspond to the parameters a, b, .
a = initial position of the object. b = .

Experiment with various values of a, b, , including negative or zero values of a,b (Not both zero!)
Keep < 6 for best graphic effect.

To run your demonstrations, simply overtype the three numbers with values of your choice, separated by commas.

> arguments := 1,2,2 :

> show_curve(arguments); HarMotion(arguments);

The first graph shows how the acceleration ( thin red curve) is opposite and proportional to the position (displacement) of the moving object
( thick red curve)
=

The second, animated graph simulates the motion of the object on the x-axis.
A small blue box on the y-axis describes the complementary harmonic motion.
Their composite motion is shown by the little red circle on the blue circular path.

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