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  4. Two pendulums have time periods T and 5T/4. They starts SHM at the same time from the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation?

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Q. Two pendulums have time periods $T$ and $5T/4$. They starts SHM at the same time from the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation?

AMUAMU 2008

Solution:

When bigger pendulum of time period $(5T/4)$ completes one vibration, the smaller pendulum will complete $(5/4)$ vibrations. It means the smaller pendulum will be leading the bigger pendulum by phase $T/4$ second
$ =\pi /2 $ rad $ =90^{\circ} $