Coupled Point Masses on a Circle

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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.

Contributed by: Enrique Zeleny (May 2013)
Open content licensed under CC BY-NC-SA



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.


[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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