A cylindrical piece of cork of density of base area A and height h floats in a liquid of density p_(l). 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).

A cylindrical piece of cork of density of base area A and height h flo

1.	A cylindrical piece of cork of density of base area A and height h floats in a liquid of density p_(l). 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).
Answer» Solution :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.