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I have one doubt which is that while swinging in sitting position if I all of sudden stands up on that sitting position and then started swinging with that same energy then does my time period will increase or decrease?

I thought that since the center of mass will rise above the ground then

$$T = 2\pi \sqrt{\frac{I}{mgd}}$$

where d = distance from center of mass to the end of that rope.

Since d will decrease (because center of mass will rise up) then time period should have been increased but I am not getting it that why it decreases.

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Time period should decrease. As $I$ goes down when the child stands up. $I$ is proportional to $d^2$, so the overall effect would be to decrease the time period when the 'length' of the pendulum goes down.

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protected by Community Mar 5 at 0:59

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