The angular frequency is a rather abstract concept which deserves some discussion.

At the most basic level, from , you should appreciate that the angular frequency *ω* is simply the frequency of the oscillation multiplied by .

At a more abstract level, from , we can think of as the phase angle of the oscillation. So *ω* is the “velocity” at which the phase of the oscillation progresses.

The angular frequency *ω* in SHM is actually very similar in concept to the angular velocity *ω* in circular motion. (This explains why they are both given the symbol *ω*.)

For oscillations, is the rate of change of phase angle.

For circular motion, is the rate of change of angular displacement.

Lastly, a circular motion collapsed into one dimension is actually an SHM. For example, the displacement in the *y*-direction of the circular motion illustrated below is actually an SHM. The circular motion’s radius *R*, is the SHM’s amplitude *R*. The angular velocity *ω* of the circular motion is also the angular frequency *ω* of the SHM.

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**Animation**

Circular Motion vs Oscillation

Pendulum Wave

**Demonstration**

Pendulum Wave (Harvard Natural Sciences)

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