Write the expression of kinetic energy and potential energy of $SHM$ particle $(i)$ as a function of displacement $(ii)$ as a function of time.

(N/A) For a particle of mass $m$ performing $SHM$ with angular frequency $\omega$ and amplitude $A$:
$(i)$ As a function of displacement $x$:
Potential Energy $(U)$: $U = \frac{1}{2} m \omega^2 x^2$
Kinetic Energy $(K)$: $K = \frac{1}{2} m \omega^2 (A^2 - x^2)$
$(ii)$ As a function of time $t$ (assuming $x = A \sin(\omega t + \phi)$):
Potential Energy $(U)$: $U = \frac{1}{2} m \omega^2 A^2 \sin^2(\omega t + \phi)$
Kinetic Energy $(K)$: $K = \frac{1}{2} m \omega^2 A^2 \cos^2(\omega t + \phi)$