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technial

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3 equal masses are connected by springs in a circle, and are confined to move in the circle. Find the eigenvalues and eigenvectors of the system.

I'm really at a bit of a loss here, I don't know whether you begin by assuming SHM occurs and get answers from there or something completely different. The question is from a general paper so you can use anything to get an answer! Any help would be greatly appreciated.

Thanks everyone.