The uniform rod of length l and mass m is suspended at its midpoint by a wire of length L. The resistance of the wire to torsion is proportional to its angle of twist θ and equals (JG/L)θ where J is the polar moment of inertia of the wire cross section and G is the shear modulus of elasticity. Derive the expression for the period  τ of oscillation of the bar when it is set into rotation about the axis of the wire.

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