Define simple harmonic motion and explain it.

(N/A) Simple Harmonic Motion $(SHM)$: The periodic motion about a fixed point on a linear path under the influence of a restoring force that acts towards the fixed point and is directly proportional to the displacement of the body from that fixed point is called Simple Harmonic Motion.
Alternatively,simple harmonic motion is a periodic motion in which the displacement is a sinusoidal function of time.
In an oscillatory motion,a restoring force is exerted towards the mean position from any point. Therefore,in simple harmonic motion,the displacement $x$ of a particle from the origin varies with time $t$ as:
$x(t) = A \cos (\omega t + \phi)$
where $A$ is the amplitude,$\omega$ is the angular frequency,and $\phi$ is the initial phase constant.
The figure shows a particle oscillating back and forth about the origin of an $X$-axis between the limits $+A$ and $-A$.