Consider a floating cylindrical buoy with radius r, height h, and uniform density (recall...

Consider a floating cylindrical buoy with radius r, height h, and uniform density (recall that the density of water is 1 g/cm3). The buoy is initially suspended at rest with its bottom at the top surface of the water and is released at time t = 0. Thereafter it is acted on by two forces: a downward gravitational force equal to its weight mg = πr2hg and (by Archimedes′ principle of buoyancy) an upward force equal to the weight πr2xg of water displaced, where x = x(t) is the depth of the bottom of the buoy beneath the surface at time t (Fig. 1). Conclude that the buoy undergoes simple harmonic motion around its equilibrium position xe = ph with period Compute p and the amplitude of the motion if p = 0.5 g/cm3, h = 200 cm, and g = 980 cm/s2.

FIGURE 1. The buoy of Problem 10.