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Question: consider pendulum consisting of a mass m attached to a...

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Consider pendulum consisting of a mass m attached to a rod of length I suspended from a central support by a hinge that is rotating at a fixed angular frequency Ω shown at right. a Show that the Lagrangian of this svstem is given bv 12 sin2 4)2 where the angle θ is the only generalized coordinate. b S how that there are two possible equilibrium angles for the system given by 90-0 and coS -1 | , where wo= -COS Here wo is the natural frequency of a simple pendulum of length l and the second equilibrium point only exists for Ω > wo- c Show that the frequencies of small oscillations about these equilibrium angles are given by ώρ cos n-

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