Analysis of 4 Equal Masses on a Circular Path

[jameson2]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[jdwood983]

Homework Statement

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.

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: \theta.

 

[jdwood983]

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