A particle executes simple harmonic oscillation with an amplitude a.The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is :

Options

A. `(T)/(8)`
B. `(T)/(12)`
C. `(T)/(2)`
D. `(T)/(4)`.

Answer

B

Explanation

We know that `Y=r sin omega t`
When `" "Y=( r )/(2)`
then `" "( r )/(2)=r sin omega t`
`(1)/(2)=sin omega t`
`impliessin((pi)/(6))=sin omega t`
`implies" "(pi)/(6)=omega t` or `(pi)/(6)=(2pi)/(T).timpliest=(T)/(12)`.
Correct choice is (b).