Question $2$: Oscillating Spring and Pendulum

Standards: SHM$,$ Oscillations, Waves, and Resonance $(2,3)$

A simple pendulum maintain correct time on Earth $(g_{\text{E}\text{a}\text{r}\text{t}\text{h}}=9\mathrm{.}8\frac{m}{s^2}).$ An eccentric astronaut takes the clock to the surface of the Moon $(g_{\text{m}\text{o}\text{o}\text{n}}=1\mathrm{.}6\frac{m}{s^2}).$

a$)$ Will the clock run slow or fast while on the Moon.

b$)$ A clock fitted with a spring balance also maintains the correct time on Earth. Will it read the correct time on the Moon?