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## Homework Statement

A plunger of mass m rests on a spring with constant k. The spring is pressed down a distance x and released from rest. How large does the the mass need to be in order to keep the plunger in contact with the spring?

## Homework Equations

PE

_{f}+KE

_{f}=PE

_{i}

kx-mg+N=0

## The Attempt at a Solution

Using the Conservation of energy equation and solving for m, I get:

kx

^{2}/(2gh+v

_{f}

^{2}) = m

I have a suspicion that I somehow have to incorporate the second equation into the answer, but am stumped as to how I proceed.