(a) Derive using Newton's laws a second-order differential equation for h(t), assuming that the only two forces acting on the cork are gravity and buoyancy. Gravity pulls the cork downward with a force equal to the mass of the cork times the gravitational constant g. Buoyancy is an upwards force felt by the cork due to water pressure, and is equal to the weight (mass times g) of the fluid displaced, according to Archimedes' principle. H h(t) (b) Suppose that the cork is pushed down and let go so that it bobs up and down in the water. According to your differential equation from the previous part, what is the period of the cork's motion? (In other words, how long does it take for the cork to complete one bob?)