velocity at any location is given as
v = w sqrt(A² - x²)
where A = amplitude , x = distance from the equilibrium position , w = angular frequency
the speed is maximum when x = 0
hence vmax = maximum speed = A w
at x = 0 , we know that the acceleration of the mass which is always directed towards the equilibrium position is zero .
hence the mass has maximum velocity at equilibrium position where the acceleration of the mass is zero.
hence the correct choice is
A. when the mass has an acceleration of zero