Understanding Simple Harmonic Motion: FAQs and Examples

[buffgilville]

Are all periodic motions simple harmonic? Why or why not? What is an example of a periodic motion that is not simple harmonic?

 

[arildno]

1. No; there's a lot of periodic motion which is not simple harmonics.
For example:
A swinging pendulum is not a simple harmonic oscillator.
The Earth's motion around the sun is periodic, but not that of a simple harmonic..

 

[quantumdude]

A simple harmonic motion function has only a single frequency, as follows:

x₁(t)=Asin(ωt)

Question: What happens when you add the following 2 harmonics together?

x(t)=x₁(t)+x₂(t)=Asin(ωt)+Asin(2ωt)

What is the period of this motion? What does the graph of x vs t look like?

The answers to those questions should get you started.

 

[arildno]

Just to state what is ordinarily meant by a PERIODIC function:
We say that a function f is periodic in t with period T, if it exists a constant T so that
f(t)=f(t+T) (for all choices of t)