$\begin{aligned} & \mathrm{T}=2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}} \\ & 0.2=2 \pi \sqrt{\frac{0.5}{\mathrm{k}}} \\ & \mathrm{k}=50 \pi^2 \\ &=500 \\ & \mathrm{x}=\mathrm{A} \sin (\omega \mathrm{t}+\varphi) \\ &=5 \mathrm{~cm} \sin \left(\frac{\omega T}{4}+0\right) \\ &=5 \mathrm{~cm} \sin \left(\frac{\pi}{2}\right) \\ &=5 \mathrm{~cm} \\ & \mathrm{PE}=\frac{1}{2} \mathrm{k} \mathrm{x}^2 \\ &=\frac{1}{2}(500)\left(\frac{5}{100}\right)^2 \\ &=0.6255\end{aligned}$