At the equilibrium position of an object vibrating on a spring, the velocity is maximal because all of the spring's potential energy is converted into kinetic energy, while the net force and acceleration are zero. The potential energy, however, is zero at this point. This is in accordance with the principles of simple harmonic motion.
When an object attached to a spring passes through the equilibrium position, its velocity is not zero because it's the point where the kinetic energy is maximized due to the conversion of elastic potential energy into kinetic energy. The net force is zero at this position, meaning that there is no acceleration happening at that moment, and the object is moving at its maximum speed. Instead, the acceleration is zero at the maximum displacement points where the spring is either fully compressed or stretched, which are the points of maximum potential energy.
As described by simple harmonic motion, the energy in an undamped system oscillates between kinetic and potential. At the equilibrium position (x = 0), all the energy of the system is kinetic, which explains why the object has velocity. At full displacement (x = A or x = -A), all the energy is potential, and the object momentarily has zero velocity as it changes direction.
The quantity that is zero at the equilibrium position is potential energy, not velocity. The object's highest velocity occurs as it passes through this equilibrium point.