b
by using formula of time period
$T=2 \pi \sqrt{\frac{m}{k}}$
$0.2=2 \pi \sqrt{\frac{0.5}{k}}$
$k=50 \pi^{2}$
$\approx 500$
$x=A\, \sin (\omega t+\phi)$
$=5\, c m\, \sin \left(\frac{\omega t}{4}+0\right)$
$=5\, {cm} \sin \left(\frac{\pi}{2}\right)$
$=5 \,{cm}$
$P E=\frac{1}{2} k x^{2}$
$=\frac{1}{2}(500)\left(\frac{5}{100}\right)^{2}$
$=0.6255$