A body performs linear S.H.M. with amplitude 'a'. When it is at a distance 3 a from extreme position, the magnitude of velocity is 3 1 times the magnitude of acceleration. The period of

Question

A body performs linear S.H.M. with amplitude 'a'. When it is at a distance 3 a ​ from extreme position, the magnitude of velocity is 3 1 ​ times the magnitude of acceleration. The period of S.H.M. is

TestHub · Accepted Answer

a = amplitude x = a − 3 a ​ = 3 2 a ​ a p ​ = ω 2 x = ω 2 3 2 a ​ v p ​ = ω a 2 − x 2 ​ = ω a 2 − 9 4 a 2 ​ ​ = ω 9 5 a 2 ​ ​ = ω 5 ​ 3 a ​ 3 v p ​ = a p ​ a p ​ v p ​ ​ = 3 1 ​ = ω 2 3 2 a ​ ω 5 ​ a /3 ​ = 2 ω 5 ​ ​ 3 = 5 ​ 2 ω ​ = 5 ​ 2 ​ × T 2 π ​ ∴ T = 3 5 ​ 4 π ​

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