Three balls are constrained to move on the circumference of a circle of radius R. The balls are connected to each other along the circumference of the circle by three identical springs with spring constant k so that in the equilibrium configuration, the springs all have their common rest length, and the balls are spaced evenly around the circle. The mass of the first ball is M; the other two balls have mass m, m<M.a) Choose as coordinates the angles a1, a2, and a3, the angular displacements of the three balls from the equilibrium configuration. Derive the Euler-Lagrange equations for the system in terms of these angles.b) Using the result of part a, find the characteristic frequencies of the system.c) What happens if m=M?

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Answers

2014-04-04T14:38:57+05:30
Answer circumference of the circle by three identical springs with spring constant k so that in the equilibrium configuration, the springs all have their common rest length, and the balls are spaced evenly around the circle. The mass of the first ball is M; the other two balls have mass m, m<M.a)  Choose as coordinates the angles a1, a2, and a3, the angular displacements of the three balls from the equilibrium configuration
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