Angular Frequency

The angular frequency is often denoted by .  The angular frequency is a constant of the motion. The angular frequency is most known in the simple harmonic motion equation (shm).

Angular frequency in simple harmonic motion equation

Note that the negative sign indicates that the acceleration is always directed towards the fixed point.

Angular Frequency and Newton's Second Law of Motion

According to Newton's second Law of Motion, the force producing the motion is proportional to the acceleration. This is given by the Newton's second Law of Motion equation:

Therefore, the restoring force of a simple harmonic motion system can be written as:

In another word, the restoring force must be proportional to the displacement from the fixed point, and directed towards the fixed point. Therefore, any oscillating system for which the restoring force meets these conditions will move in simple harmonic motion.