Periodic Motion

Periodic motion is any motion that repeats at regular time intervals. A swing moves back and forth through the same arc repeatedly. A ball being dribbled bounces up and down in a repeating pattern. The Earth orbiting the Sun completes the same circular path every year. Each exhibits periodic motion because the motion pattern repeats at regular time intervals.

Simple Harmonic Motion (SHM)

Simple harmonic motion is a special type of periodic motion. In SHM, an object moves back and forth, or oscillates, through a central point called the equilibrium position. The displacement $x$ from equilibrium varies smoothly between $+A$ and $-A$, where $A$ is called the amplitude.

Not all periodic motion is SHM. Consider three examples:

A mass on a spring oscillates smoothly through its equilibrium position. This is the classic example of SHM.

A bouncing ball repeats periodically, but it reverses abruptly at the floor rather than changing direction smoothly. This is periodic but not SHM.

Uniform circular motion is periodic, but there is no oscillation through a central equilibrium. The object moves around a circle, not back and forth. This is also not SHM.

However, if we look only at displacement along one direction during circular motion, that is SHM.