Write the formula for the instantaneous velocity of a particle performing $SHM$ along the $X$-axis.

(N/A) For a particle performing $SHM$ along the $X$-axis,the displacement is given by $x(t) = A \sin(\omega t + \phi)$,where $A$ is the amplitude,$\omega$ is the angular frequency,and $\phi$ is the initial phase constant.
The instantaneous velocity $v(t)$ is the time derivative of the displacement $x(t)$:
$v(t) = \frac{dx}{dt} = \frac{d}{dt} [A \sin(\omega t + \phi)]$
$v(t) = A \omega \cos(\omega t + \phi)$
Alternatively,expressing velocity in terms of displacement $x$:
$v = \pm \omega \sqrt{A^2 - x^2}$