A particle of mass m is attached to a light, inextensible string of length a. With the

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A particle of mass m is attached to a light, inextensible string of length a. With the other end of the string attached to a fixed point, A, the particle rests in equilibrium. The particle is then given an initial horizontal speed U. Find the condition on u such that the particle never leaves the circular path, but never completes full circles.

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