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:

Let displacement equation of particle executing SHM is y = a sin ωtAs particle travels half of the amplitude from the equilibrium position, so y = a2Therefore, a2 = a sin ωtor sin ωt = 12= sin π6 or ωt = π6or t = π6ω or t = π6(2πT)(as ω = 2πT)or t = T12Hence, the particle travels half of the amplitude from the equilibrium in T12sec