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If you take a rope and fix the top end and allow the rope to swing, then it is just a pendulum and the period of swing is widely known (and on wikipedia) as approx. T = 2*pi*(L/g)^0.5 where L is the length of the pendulum and g is gravity.

My question is: What if I take both ends of the rope and fix them (like tying them to an overhead horizontal metal bar), like a playground swing. How do you calculate the period of swing then? In this case the "length of the pendulum" would vary - it would go from 0 at the fixed ends to the maximum at the saggiest part of the rope.

This problem seems really simple but I can't figure it out!!! Any help would be greatly appreciated. Thanks a lot!

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# Period of swing of a rope with two fixed ends

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