The displacement of particle in S.H.M. is x=A ( t+ / 6) . Its speed will be maximum at time ( Sin 90^ =1 )

Step-by-step solution

The displacement of the particle undergoing simple harmonic motion is given by x = A ( t + 6 ) Differentiation yields the velocity function: v = -A ( t + 6 ) where speed is the magnitude |v| , requiring | ( t + /6)| = 1 for maximum value. This maximum first occurs at the smallest positive argument where ( ) = 1 , corresponding to = /2 . Setting t + /6 = /2 gives t = /3 , yielding t = /(3 ) . Maximum speed is achieved at time t = 3 s . Answer: A