A point performs simple harmonic oscillation of period T and the equation of motion is given by x=a ( t+ 6 ) . After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

Step-by-step solution

Key Idea : Velocity is the time derivative of displacement. Writing the given equation of a point performing SHM x=a ( t+ 6 ) Differentiating Eq. (i), w.r.t. time, we obtain y= d x d t =a ( t+ 6 ) It is given that y= a 2 , so that or a 2 =a ( t+ 6 ) 1 2 = ( t+ 6 ) or 3 = ( t+ 6 ) array ll or & t+ 6 = 3 & t= 6 or & t= 6 = T 6 2 = T 12 array Thus, at T 12 velocity of the point will be equal to half of its maximum velocity.