Calculating the Period of Small Oscillations for a Floating Object

[Varnson]

[SOLVED] Mechnics - Small Oscillations

Homework Statement

A body of uniform cross-sectional are A= 1cm^2 and a mass of density p= 0.8g/cm^3floats in a liquid of density po=1g/cm^3 and at equilibrium displaces a volume of V=0.8cm^3. Show that the period of small oscillations about the equilibrium position is given by t = 2*pi*(v/gA)^.5 where g is the gravitational field strength. Determine the value of t.

Homework Equations

The Attempt at a Solution

I am totally lost on this one. I am thinking that I would need to find the mass of the object, which is simple because the density and volume are given. What do I do after that?

 

[siddharth]

i) At equilibrium, what are the forces acting on the object?
ii) If you displace the object by a small amount from the equilibrium position, what's the restoring force?
iii) Is this a type of Simple harmonic motion for small displacements?

 

[Varnson]

I figured it out, thanks for the pointers!