Potential energy of spring and mass system

1. Nov 16, 2013

rmfw

1. The problem statement, all variables and given/known data

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

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

What is the potential of the system?

3. 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

Last edited: Nov 16, 2013
2. Nov 16, 2013

Staff: Mentor

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?

3. Nov 16, 2013

rmfw

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

got it