Spring constant for a solid not in equilibrium in a fluid

[Twoism]

Homework Statement

A cylinder of density RhoO, length L, and cross-section area A floats in a liquid of density RhoF with its axis perpendicular to the surface. Length h of the cylinder is submerged when the cylinder floats at rest. Suppose the cylinder is distance y above its equilibrium position. Find an expression for Fnet (in the y direction). Use what you know to cancel terms and write this expresion as simple as possible. What is the "spring constant" k? I go on to prove h=(RhoO/RhoF)L

Homework Equations

Fnet=F(buoyant) + -(F(cylinder))
F(buoyant)=RhoF*VolumeInWater*g
F(cylinder)=RhoO*TotalVolume*g
Fnet=-ky
VolumeInWater=A(h-y)
TotalVolume=AL
h=(RhoO/RhoF)L
k= Spring constant

The Attempt at a Solution

I get to a point where the equation goes as follows
-ky=Ag(RhoF(h-y) - (RhoO*L))
I tried substituting in h=(RhoO/RhoF)L and L=(RhoF/RhoO)h, but neither seem to make the expression "simple" like the problem states, and when I solve for k, it's just messier. Thanks for any help. Oh, and the LaTeX kept messing up, so I had skip it, sorry.

 

[rl.bhat]

From the equilibrium position if you press the cylinder fro a small distance dy,
weight of the displaced liquid is A*g*ρf*dy = buoyant force = -k*dy.

So k = A*g*ρf.

Put it in the final expression and simplify.

 

[Twoism]

From the equilibrium position if you press the cylinder fro a small distance dy,
weight of the displaced liquid is A*g*ρf*dy = buoyant force = -k*dy.

So k = A*g*ρf.

Put it in the final expression and simplify.

You're pulling it up though, not pressing it down, if that makes a difference. Also, I'm slightly confused because how can the buoyant force equal the restoring force if the there's already part of the cylinder in the water. The length of the cylinder in the fluid isn't just dy. Wouldn't it be h+dy (if you're pressing it down), which would make
A*g*ρf*(h+dy)=-k*dy

Right?

EDIT: Nevermind, I understand now. If you did h+dy, that would be implying the equilibrium point is at the surface of the fluid, which it is not. I don't know why I was thinking that the rest of the buoyant force would contribute to the restoring force if it was in equilibrium at length dy away. Thank you!