A cylindrical piece of cork of base area A and height h floats in a liquid of density `rho_(1)`. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period
`T=2pisqrt((hrho)/(rho_(1)g))`

Explanation

In equilibrium, weight of the cork equals upthrust. When the cork is depressed slightly by an amount x, net upward force is `Axp_(1)`g.
Thus the force constant `k = Ap_(1)g`
and m = Ahp, where p is the density of the cork.
Now `T = 2pisqrt((m)/(k))`
or `T = 2pisqrt((Ahp)/(Ap_(1)g))`
or `T = 2pi sqrt((hp)/(p_(1)g))`