Buoy in water differential equation finding weight

[colonelone]

Homework Statement

A cylindrical buoy with diameter 18 in. floats in water with its axis vertical. When depressed slightly its period of vibration is found to be 2.7 seconds. Find the weight of the cylinder.

Homework Equations

I know that an object submerged in water is buoyed up by a force equal to the product of density and volume, and the density of water is given as 62.5 lb/ft³

The Attempt at a Solution

Treating it as a spring problem

Weight of buoyancy force = density * volume = (62.5 lb/ft³) * volume
Period = 2(pi) sqrt (m/k) = 2.7sec
k = mass / distance stretched
volume = (pi) (r)²h

Since Period (T) 2.7sec then is this valid?

2.7 = 2(pi) sqrt (m/k) --> (2.7/(2pi)²= (m/k)
and since k = m/d --> (2.7/(2pi)² = d
so d = 0.1846578572 ?

So would this d become the height for volume? Because that gives me 46.98970118, which multiplied with 62.5 gives 2936.856324, which I know isn't right.

 

[colonelone]

Anybody?