A cubical block of side length L has a density Dc and floats in a liquid of density Dl with a small part of the block above the liquid's surface. Please derive the following in terms of these parameters and constants:
a) Determine the fraction of the volume of the block that is below the liquid's surface.
b) The block is now pushed downward with a small displacement x and released from rest. Show that the resulting motion of the block is simple harmonic and determine the period of oscillation.