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A particle executing SHM with time period T and amplitude A. The mean velocity of the particle averaged over quarter oscillation, isA. `(A)/(4T)`B. `(2A)/(T)`C. `(3A)/(T)`D. `(4A)/(T)` |
Answer» Correct Answer - D Let the displacement off the particle executing SHM at any instant t is, `x=Asinomegat` Velocity, `v=(dx)/(dt)=(d)/(dt)Asinomegat=Aomegacosomegat` The mean velocity of the particle averaged over quarter oscillation is `ltvgt_(0toT//4)=(int_(0)^(T//4)vdt)/(int_(0)^(T//4)dt)=(int_(0)^(T//4)Aomegacosomegatdt)/(T//4)` `((Aomega)/(omega)[sinomegat]_(0)^(T//4))/(T//4)=(A[sinomegat]_(0)^(T//4))/(T//4)=(4A)/(T)` |
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