Two pendulums have time periods T and 5T/4. T | vedclass

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(A) Let the time periods be $T_1 = T$ and $T_2 = 5T/4$.For the pendulums to be in the same phase again,the time elapsed $t$ must be an integer multipl

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$5$

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(A) Let the time periods be $T_1 = T$ and $T_2 = 5T/4$.For the pendulums to be in the same phase again,the time elapsed $t$ must be an integer multiple of both time periods.$t = n_1 T_1 = n_2 T_2$,where $n_1$ and $n_2$ are the number of oscillations.$n_1 T = n_2 (5T/4)$.$n_1 = n_2 (5/4) \implies n_1/n_2 = 5/4$.Since $T_1 For the smaller pendulum to complete its oscillations,$n_1 = 5$ and $n_2 = 4$.Thus,after $5$ oscillations of the smaller pendulum,they will be in the same phase.

Two pendulums have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum will they be again in the same phase?

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