Q. Two simple pendulums whose lengths are and are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum, will be the two be in phase again?

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Solution:

The time period of a simple penduium is

where, is length.

Given,
.
In a given time shorter penduium will make one oscillation more than the longer.
Let after oscillations, the pendulums are in same phase, then