A particle executing a simple harmonic motion has a period of 6 sec.The time taken by the particle to move from the mean position to half the amplitude is

Options

A. `(3)/(2)sec`
B. `(1)/(2)Sec`
C. `(3)/(4)sec`
D. `(1)/(4)` sec

Answer

B

Explanation

Since the motion is started from the mean position,therefore displacement x of a particle executing SHM at ant time t from its mean position is given by
`x=Asinomegat`
At `x=(A)/(2)`
`therefore (A)/(2)=Asinomegatimplies(1)/(2)=sinomegat`
`sin((pi)/(6))=sinomegatimplies(pi)/(6)=omegat`
`t=(pi)/(6omega)=(pi)/((6(2pi)/(T))) (thereforeomega=(2pi)/(T))`
`=(T)/(12)=(6)/(12)=(1)/(2)S(because T=6 S(Given))`