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

Step-by-step solution

Let displacement equation of particle executing SHM is y=a t As particle travels half of the amplitude from the equilibrium position, so y= a 2 Therefore, a 2 =a t or t= 1 2 = 6 or t= 6 ort= 6 or t= 6 ( 2 T ) ( as = 2 T ) or t= T 12 Hence, the particle travels half of the amplitude from the equilibrium in T 12 ~s .