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The Link between Circular Motion and

Simple Harmonic Motion

If you observe a body rotating uniformly in a circle from a side perspective (in one plane only) it exhibits SHM.

This means that the equations we had relating to circular motion and angular velocity can be used to describe SHM:

The angular velocity ω becomes the angular frequecy of the SHM

So,

ω =2π/T

and

ω = 2πf