How large initial angular velocity is needed for pendulum to go completely around?

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If a pendulum is initially at its unstable equilibrium position, how large an initial angular velocity is necessary for it to go completely around?

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Any non-zero velocity will do it, if you assume no friction or other dissipation forces. By conservation of energy it will reach the initial position after one turn with that same speed, and will keep rotating around forever. The maximum speed will be at the bottom, and the smallest speed at the top.