Displacement time equation of a particle executing SHM is `x=a sin (wt+pi //6)` . Time taken by the particle to go directly from `x=-A//2 "to" x=+A//2` is

Explanation

Period of oscillation is `T=(2pi)/(omega)`
Now time taken in going from mean position to `x=A/2` or from `x=A/2` to mean position comes out to be `T/12`. Therefore the desired time will be
`t=2(T/12)=T/6=(pi)/(3pomega)`