(a) A thin uniform rod of length 2b is suspended by two vertical light strings, both of fixed length 1, fastened to the ceiling. Assuming only small displacements from equilibrium, find the Lagrangian of the system and the normal frequencies. Find and describe the normal modes. [Hint: A possible choice of generalized coordinates would be x, the longitudinal displacement of the rod, and yi and y2, the sideways displacements of the rod's two ends. You'll need to find how high the two ends are above their equilibrium height and what angle the rod has turned through.]

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