Harmonic motion

There is a peculiar type of motion that is worth discussion: Simple Harmonic Motion (SHM).

SHM refers to a regular oscillation, such as you might see with a pendulum or mass bobbing up and down (or back and forth) on a spring.

http://www.walter-fendt.de/ph14e/pendulum.htm

Note in this applet that while the "bob" swings back and forth, the displacement (elongation) changes SINUSOIDALLY, as shown on the graph. The velocity and acceleration of the bob also changes in a similar fashion.

Note the similar behavior for a mass on a spring:

http://www.walter-fendt.de/ph14e/springpendulum.htm

This type of motion is called "Simple Harmonic Motion," and it assumes the following reasonable conditions:

- the initial amount of pull (as long as it is "small") does not matter
- the mass of the string (for a pendulum) is small compared to the bob
- there are no significant frictional losses or effects

If these conditions are not met, the oscillator would likely be a complex harmonic oscillator, and there are different rules for those!

I introduce the idea of SHM, as it leads us nicely into the concept of a wave. If you imagine a mass bobbing up and down on a spring, and can imagine a pen attached to the mass, it could draw out the shape of the graph above. You would have to have the pen hit a piece of paper that is being moved at a constant speed horizontally.

In this case, a sine wave would be generated. You can see a little of this here:

http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html