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## Homework Statement

Find the total potential energy described by a system consisting of a mass hanging by a spring, connected to a second mass also hanging by a spring. Assume that the masses are the same, and the springs are identical (in spring constant and length).

## Homework Equations

[tex]V_{spring} = \frac{1}{2} k y^{2}[/tex]

[tex]V_{gravity} = -mgy[/tex]

## The Attempt at a Solution

This is one-dimensional, so I'm working only with "y". I'm calling "up" the positive y-direction, and I'm labeling the top mass "1" and the bottom mass "2".

The initial position of mass 1 will be [itex]y_{01}[/itex] and the initial position of mass 2 will be [itex]y_{02}[/itex].

I'm assuming that (is this right?):

[tex]V_{total} = V_{spring,1} + V_{spring,2} + V_{gravity,1} + V_{gravity,2}[/tex]

So shouldn't the answer just be:

[tex]V_{total} = \frac{1}{2} k (y_{1} - y_{01})^{2} + \frac{1}{2} k [(y_{2}-y_{02})-(y_{1}-y_{01})]^{2} - mgy_{1} - mgy_{2}[/tex]

But this can't be right! Since they're both conservative forces (gravity and the springs), doesn't the derivative need to vanish when evaluated at the initial values? It doesn't for the gravity potential parts. Help!