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1. A uniform thin rigid rod of length L, mass M, is suspended by two identical springs attached at the ends of the rod. In equilibrium the rod is horizontal. Assume the motion is restricted so that the rod stays in one vertical plane and in the limit of small oscillations the ends of the rod only move up and down. The moment of inertial for a thin rod about its center is ML-/12 . (a) Using the Lagrangian method, write the second-order differential equation(s) of motion for the bar appropriate for k M small motions from equilibrium. (b) What are the two normal mode frequencies