Show that the motion of a simple pendulum is simple Harmonic ,hence drive it's time period

Suppose you use a machine that gives you a mechanical advantage of 2 to achieve an output force of 30newtons what must the input force be

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

Which changes of state do the labels represent? a: b: c: