(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

|--------------------|

m|----------m-------- |m

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-------> x : positive x axis

This is a picture of a coupled oscillator in equilibrium. All three masses are equal and the spring constant on the long springs are k and the two short middle springs is κ. the displacement of the three masses are defined as x1, x2, x3.

2. Relevant equations

L=T-U

T=1/2 m (xdot)^2

U= 1/2kx^2

3. The attempt at a solution

I am having trouble with the lagrangian for this problem, mostly with the sign of the coefficients. I think that the kinetic energy T= 1/2 m((x1dot)^2+(x2dot)^2+(x3dot)^2)

and the potential U= 1/2 [kx1^2 + 2κx2^2 + kx3^2 ] .

is this the correct approach?

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# Lagrangian for Coupled Ocillator problem

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