For simple pendulum: $T =2 \pi \sqrt{\frac{\ell}{ g }}$ As g will decrease on moon, time period will increase
For spring mass system : $T=2 \pi \sqrt{\frac{m}{k}}$
It will not change and remains the same

$x = a\,\sin \,\left( {\omega t + \pi /6} \right)$
After the elapse of what fraction of the time period the velocity of the particle will be equal to half of its maximum velocity?