Simple Harmonic motion of buoyant force

[Jake4]

Homework Statement

a cylinder is in a deep pool of liquid. it has mass 2kg, diameter 10cm, height 15cm. the density of the liquid is 1.5g/cm^3. The cylinder is submerged up to 12cm, and let go. Show that the resulting motion is simple harmonic.

Homework Equations

x=Acos(wt)

buoyant force = M(of displaced water) * g

 

[grzz]

Draw a FBD with all forces acting on system.

 

[Jake4]

i drew a fbd, and that got me F= F(buoyant)-mg

thats as far as I can get... I've never felt so lost in a physics problem, i don't even know where to start...

 

[grzz]

Try to find the position of equilibrium first.