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Normal coordinates and frequencies of four masses connected by springs on a circle

  1. Nov 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Given the system of 4 equal masses connected by identical springs, and constrained to move on a circle, find the normal coordinates and frequencies of the masses.

    I'm not looking for the answer, just a push in the right direction as I'm having trouble starting. If someone could explain how this is related to the motion of springs and masses in a straight line system, it would be much appreciated.
    Even a vague idea would be helpful, thanks.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 24, 2009 #2
    Re: Normal coordinates and frequencies of four masses connected by springs on a circl

    It's not really related to motions of the mass-spring system in 1D. You might want to consider spherical-polar coordinates with the origin at the center of the circular loop, that way the masses are given by a single coordinate: [itex]\theta[/itex].
     
  4. Nov 24, 2009 #3
    Re: Normal coordinates and frequencies of four masses connected by springs on a circl

    I should note that you will actually have 4 [itex]\theta[/itex] coordinates, one for each mass. I hope I didn't introduce any confusion on that.
     
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