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.
