Consider a floating cylindrical buoy with radius r and height h of uniform density 0.5g/cm3 (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 t = 0. Thereafter it is acted upon by two forces: a downward gravitational force equal to its weight mg = r2hg, and an upward buoyancy force equal to the weight of the water it displaces r2xg, where x(t) is the depth of the bottom of the buoy beneath the surface

at time t.

1. (a)Set up a differential equation describing the motion of the buoy with respect to
2. time. (Ignore water resistance).
3. (b)Nonzero solutions to the differential equation above should display oscillatory
4. behavior. What is the period of the oscillation (in terms of r, h, g, )?
5. (c)Find the solution given the constants = 0.5 g/cm3, h = 200 cm, r = 10 cm, and g = 980 cm/s2.