(Solution) - A mass spring ring consists of n masses connected in a -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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A mass-spring ring consists of n masses connected in a circle by n identical springs, and the masses are only allowed to move in the angular direction.
(a) Derive the equations of equilibrium.
(b) Discuss stability, and characterize the external forces that will maintain equilibrium.
(c) Find such a set of nonzero external forces in the case of a four mass ring and solve the equilibrium equations. What does the nonuniqueness of the solution represent?