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Three point like masses, all of them equal to $m$, and two massless springs (constant $k$) connecting  them are constrained to move in a frictionless tube of radius $R$. The system is in gravitational field as shown in figure. The springs are of zero length and the masses  may move through one another. Using Lagrangian methods, find the normal modes of small vibration about the position of equilibrium of this system and describe each of the modes.

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