Simple Harmonic Motion (SHM)

Definition

A motion is called simple harmonic motion if the restoring force is directly proportional to displacement and directed toward the equilibrium position.

Mathematical Condition

$$ F = -kx $$

Using Newton’s second law:

$$ m\frac{d^2 x}{dt^2} = -kx $$

Differential Equation of SHM

$$ \frac{d^2 x}{dt^2} + \omega^2 x = 0 $$

Where:

$$ \omega = \sqrt{\frac{k}{m}} $$