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

jameson2

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

jdwood983

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].

jdwood983

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.