$2 \frac{\mathrm{d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+32 \mathrm{x}=0 \quad \mathrm{OR}$

$\frac{d^{2} x}{d t^{2}}+\frac{32}{2} x=0$

$\frac{d^{2} x}{d t^{2}}=-16 x$         $...(i)$

The standard equation of $SHM$ is,

$\frac{d^{2} x}{d t^{2}}=-\omega^{2} x$       $...(ii)$

Comparing equation, $(i)$ and $(ii),$ we get

$\omega^{2}=16 \quad \mathrm{OR}$   $\omega=4$

The period, $T=\frac{2 \pi}{\omega}=\frac{2 \pi}{4}=\frac{\pi}{2} \mathrm{s}$