A cylinder of radius r, height h, and mass m floats with its axis vertical in a liquid of density pas shown in the following figure. Archimedes' Principle: An object partially or totally submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced. h x(1) Equilibrium Position Liquid Level 1. Set up the differential equation governing the displacement x(t), measured relative to the equilibrium position, and determine the period of oscillation. 2. If the cylinder is set into oscillation by being pushed down a displacement xo at t= 0 and then released, determine the response x(t).