Finding x for a spring using energy equations

[cbasst]

Homework Statement

This isn't a homework question, just something I've been thinking about. If given a situation in which mass m is hung on a spring with constant k, I know you can set the spring force equal to the weight of the mass to find how far it stretches. Is there a way to find how far it stretches using energy equations? It seems like it should be doable, but I can't figure out how.

Homework Equations

w = mg
F = -kx
ΔU_g = mgh
U_s = kx²/2

The Attempt at a Solution

As I said, setting mg = kx can solve for x. How do I do it with energy though?
U_g = U_s
mgx = kx²/2

But now I get a different answer for x. What did I do wrong with the energy equations?

 

[Infrared]

The energy approach will give you the farthest the mass on the spring will fall. This is not the equilibrium position. Think about it, if I let the mass drop, then when it passes the equilibrium position, it will not have zero velocity.

 

[cbasst]

Ah. This makes sense now! Thanks!