Coupled Point Masses on a Circle

This Demonstration solves a system of four point masses connected with springs constrained to lie on a circular ring. Qualitatively, you can observe uniform rotation and in-phase and out-of-phase vibration, but the crossings and overlappings in the solutions are unphysical and not mentioned in textbooks.

SNAPSHOTS

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DETAILS

For four masses, the equations of motion are
,
,
,
,
where is the position of the mass from its equilibrium position, is the mass of each pont, and is the spring constant.
Reference
[1] W. Greiner, Classical Mechanics: Systems of Particles and Hamiltonian Dynamics, 2nd ed., New York: Springer-Verlag, 2010 pp. 295–297.
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