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Question
A simple pendulum performs S.H.M. of period 4 seconds. How much time after crossing the mean position, will the displacement of the bob be one-third of its amplitude.
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Solution
Data: T= 4 s, x = A/3
The displacement of a particle starting into SHM from the mean position is x = A sin wt = A sin `(2π)/"T"`t
∴ A sin `(2π)/"T"`t = `"A"/3`
∴ `(2π)/"T"`t = sin-1 0.3333 = 19.47° = `19.47xxπ/180`rad
∴ `2/4`t = `19.47/180`
∴ t = `19.47/90` = 0.2163 s
∴ The displacement of the bob will be one-third of its amplitude 0.2163 s after crossing the mean position.
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