For a mass $m$ attached to an ideal spring of constant $k$, the restoring force is $F=-kx$. Equating it to $ma$: $m\frac{d^{2}x}{d{t}^2}=-kx⟹\frac{d^{2}x}{d{t}^2}+\left(\frac{k}{m}\right)x=0$ Comparing with the standard SHM equation $\frac{d^{2}x}{d{t}^2}+{\omega }^{2}x=0$, we find: $\omega =\sqrt{\frac{k}{m}}$ The time period $T$ is given by $T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{m}{k}}$.