A cylindrical piece of cork of density of base area A and height h floats in a liquid of density `p_(1)`. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period
`T=2pisqrt((hp)/(p_(1)g))`
where p is the density of cork. (Ignore damping due to viscosity of the liquid).

Explanation

In equilibrium, weight of the cork equals the up thrust. When the cork is depressed by an amount x, the net upward force is `Axp_(1)g`. Thus the force constant `k = Ap_(1)g `. Using m = Ahp, and `T=2pisqrt(m/k)` one gets the given expression.