Potential energy of spring and mass system

[rmfw]

Homework Statement

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There are 3 equal masses connected by springs with length a and spring constant k.

The system can only move in the x axis.
x1,x2,x3 is the position of each massWhat is the potential of the system?

The Attempt at a Solution

I came up with this equation:

$U=\frac{1}{2} k [(a-x2-x1)^2 + (a-x3-x2)^2]$

is it right? thanks

 

[mfb]

Try x_1 = -100, x_2 = -99, a=1 (in meters if you like). Clearly the spring between 1 and 2 is not stretched (it has rest length 1 and the distance between the points is 1). What does your function give for that spring? Can that be right?

 

[rmfw]

$U=\frac{1}{2} k [(x2-x1-a)^2 + (x3-x2-a)^2]$

got it