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Eigenstates of masses on springs

  1. Nov 21, 2009 #1
    Hello, I am a having a problem finding the solution of the follow:

    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.
     
  2. jcsd
  3. Nov 22, 2009 #2

    tiny-tim

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    Hello technial! :smile:

    Call the spring lengths θ φ and (2π - θ - φ).

    Do F = ma on each mass, and you should end up with an equation in θ'' φ" θ and φ which I suspect (i haven't worked it out) will be separable into two x'' = -kx equations with x (I'm guessing) = θ ± φ.

    So no need to make assumptions :wink: … the SHM should come out of the elementary F = ma equations.

    What do you get? :smile:
     
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