A particle executes S.H.M. starting from its mean position at t = 0. If its velocity is $\sqrt{3}$b$\mathrm{\omega }$, when it is at a distance b from the mean position, when $\mathrm{\omega }$ = 2$\mathrm{\pi }$/T, the time taken by the particle to move from b to the extreme position on the same side is.