Question

A cylindrical piece of cork of density of base area A and height h floats in a liquid of density ρt. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a T = 2π \(\sqrt \frac{hρ}{ρ1g}\)where ρ is the density of cork. (Ignore damping due to viscosity of the liquid). 

Answer 1

Initially in equilibrium, 

weight of cork = weight of water displaced

When cork is pushed in, then the restoring force acting on it is : 

f = – weight of the portion dipped after pushing