Question

What is the difference between periodic motion and circular motion

Answer 1

circular motion never reaches the origin 0,0.
The two are actually very similar; both have a period, for circular motion this is a period of revolution, for periodic motion (or simple harmonic motion) this is the period of returning to the horizontal axis. imagine tracing periodic motion and the n having it move at a constant speed horizontally, it would look like a sine wave. The equation for a sine wave is y = sin x. The equation for a circle is
y=r sin x.

if you rotate circular motion so as to look at it from the side you would see periodic motion. The point is that circular motion is measured around a radius and periodic motion doesn't.