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  4. Two pendulums of time period 3s and 7s respectively start oscillating simultaneously from two opposite extreme positions. After how much least time they will be in phase

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Q. Two pendulums of time period $3s$ and $7s$ respectively start oscillating simultaneously from two opposite extreme positions. After how much least time they will be in phase

NTA AbhyasNTA Abhyas 2020

Solution:

Let they will meet in phase after time $'t'$ .
Then $\phi_{1}-\phi_{2}=\pi \frac{2 \pi }{T_{1}}t-\frac{2 \pi }{T_{2}}t=\pi \Rightarrow t=\frac{21}{8}s$