In Simple Harmonic Motion (SHM), the relation between velocity and amplitude depends on the phase of the motion.
In SHM, an oscillating system moves back and forth about a stable equilibrium position with a motion that can be described by a sinusoidal function. The amplitude of the motion represents the maximum displacement from the equilibrium position, while velocity represents the rate of change of displacement with respect to time.
At the extreme points of the motion, where the displacement is maximum (equal to the amplitude), the velocity of the system is zero. This occurs when the system reaches the turning points of its motion and changes direction. At these points, the restoring force acting on the system is at its maximum, causing the velocity to momentarily become zero before changing direction.
On the other hand, at the equilibrium position, where the displacement is zero, the velocity of the system is at its maximum. This occurs because the restoring force is also zero at the equilibrium position, allowing the system to reach its maximum velocity before slowing down and reversing its motion.
In summary, in SHM, the velocity is zero at the extreme points of the motion (maximum displacement), while it is at its maximum at the equilibrium position (zero displacement). The relation between velocity and amplitude is such that they are out of phase by 90 degrees. When the displacement is maximum, the velocity is zero, and vice versa.