Define simple harmonic motion. Write important characteristics of simple harmonic motion.

(N/A) Simple Harmonic Motion $(SHM)$ is a special type of periodic motion where the restoring force is directly proportional to the displacement from the mean position and is always directed towards the mean position. Mathematically,$F = -kx$,where $k$ is the force constant and $x$ is the displacement.
Important characteristics of $SHM$ are:
$1$. The motion is periodic and oscillatory.
$2$. The restoring force is always proportional to the displacement $(F \propto -x)$.
$3$. The acceleration of the particle is proportional to the displacement and directed towards the mean position $(a = -\omega^2 x)$.
$4$. The total mechanical energy of the system remains conserved.
$5$. The motion can be represented by a sine or cosine function,such as $x(t) = A \sin(\omega t + \phi)$.