2 discs connected by spring, airborne?

[alindao]

Homework Statement

2 identical discs each mass m are connected to stiff spring with constant k. when you push down on the top disc and release, will the system be able to lift off ground. if so, how high?

Homework Equations

f=ma,f=kx,pe=mgh,pe=1/2kxsquared, ke=1/2mvsquared

The Attempt at a Solution

1/2kxsquared=mgh
h=1/2kxsquared/(mg)

 

[haruspex]

h=1/2kxsquared/(mg)

That assumes all the spring potential energy gets converted to gravitational energy. Will that happen?