c
$\mathrm{U}=4(1-\cos 2 \mathrm{x})$
$\because F=-\frac{d U}{d x} \Rightarrow F=-8 \sin 2 x$
For small oscillations, $x$ will be small hence
$F=-8(2 x)=-16 x \quad \Rightarrow k=16$ and $m=1 \mathrm{kg}$
$\therefore \omega^{2}=\frac{\mathrm{k}}{\mathrm{m}}=\frac{16}{1}=16 \Rightarrow \omega=4$
$\Rightarrow \mathrm{T}=\frac{2 \pi}{\omega}=\frac{2 \pi}{4}=\frac{\pi}{2}$