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So here is a crazy problem for you all. Imagine there is a system of three balls in a line. The first and last balls have a larger mass M and the middle ball is a smaller mass m. Inbetwen the two larger balls and the middle ball are springs with spring constant of k. Now I would like to model this confusing heap of a system and solve the resulting eigenvalue problem . Trouble is, I don't k ow where to start. Normally, I would set up a differential relation, but since none of the balls are connected to walls, I don't know what is moving where? The problem doesn't even mention an external force. Also, what aould the eigenvalue solution to this problem even mean? I can't seem to grasp the meaning behind this problem. Please help.

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