Physics - unit d simple harmonic motion

Simple Harmonic Motion (SHM) is a specific type of periodic motion where the restoring force acting on a system is directly proportional to the displacement of the system from its equilibrium position and acts in the direction opposite to the displacement. This proportionality is encapsulated by Hooke's Law for elastic systems.

2.1 Defining Characteristics & Conditions:

The defining characteristic of SHM is satisfied when the acceleration $a(t)$ of the oscillating body is directly proportional to its displacement $x(t)$ from the equilibrium position and is oppositely directed:
$$ a(t) = - \omega^2 x(t) $$
where $\omega$ is the angular frequency (in rad/s), a positive constant characteristic of the system.