A particle is executing SHM of periodic time T the time taken by a particle in moving from mean position to half the maximum displacement is `(sin 30^(@)=0.5)`

Options

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

Answer

D

Explanation

If the particle at t = 0 s is at mean position, the maximum displacement is given by, `x = A "sin"(2 pi t)/(T)`
If it takes time `t_(1)` to move from mean position to half the displacement, then
`(A)/(2)=A"sin"(2pit)/(T)`
or `(1)/(2)="sin"(2pit)/(T)`
or `sin 30^(@) = "sin"(2 pi t)/(T)" "[because sin 30^(@) = (1)/(2)]`
or `"sin"(pi)/(6)="sin"(2pit)/(T)or (pi)/(6)=(2pit)/(T)`
`rArr" "t = (T)/(12)s`