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

We know that displacement of a particle executing SHM is given by
`y=r sin omega t`
`:." "( r )/(2)=r sin((2pi)/(T).t)`
`(1)/(2)=sin((2pi)/(T).t)`
`implies" "(2pi)/(T).t=(pi)/(6)`
`implies" "t=(T)/(12)`
`t=(6)/(12)=(1)/(2)s`
So correct choice is b.