Figure illustrates a cylindrical buoy floating in water with a mass density (. Assume that the center of mass of the buoy is deep enough so that the buoy motion is primarily vertical. The buoy mass is m and the diameter is D. Archimedes' principle states that the buoyancy force acting on a floating object equals the weight of the liquid displaced by the object,
(a) Derive the equation of motion in terms of the variable x, which is the displacement from the equilibrium position,
(b) Obtain the expression for the buoy's natural frequency,
(c) Compute the period of oscillation if the buoy diameter is 2 ft and the buoy weighs KMX) lb Take the mass density of fresh water to be ( = 1.94 slug/ft3.