During the S.H.M of simple pendulum, when the bob comes back to its mean position, the displacement gradually decreases, and eventully becomes zero at the equilibrium position, while it is said that its velocity is still maximum despite of zero displacement, then how is it possible for a body to have max.velocity with zero dis?

if one measures displacement in the vertical, and velocity in the direction it is going, then at the bottom position, vertical displacement is zero, and velocity is maximum.

To understand how a simple pendulum can have maximum velocity at the equilibrium position despite having zero displacement, let's analyze the motion in more detail.

A simple pendulum undergoes Simple Harmonic Motion (SHM), which means the bob oscillates back and forth around its mean position. When the bob reaches its maximum displacement on one side, it starts moving back towards the mean position. At the mean position (equilibrium position), the displacement becomes zero.

Although the displacement is zero at the equilibrium position, the bob still possesses maximum velocity. This may seem counterintuitive, but it can be explained using the principles of SHM.

During the pendulum's motion, energy is constantly interchanging between potential energy and kinetic energy. As the bob moves towards the equilibrium position, its potential energy decreases and is converted into kinetic energy. By the time it reaches the equilibrium position, all of its initial potential energy is converted into kinetic energy. This results in maximum velocity at the equilibrium position since kinetic energy is directly proportional to the square of velocity.

When the bob moves away from the equilibrium position, the process reverses. Kinetic energy decreases and is converted back into potential energy until the bob reaches its maximum displacement on the opposite side. The cycle then repeats as the pendulum oscillates back and forth.

So, while the displacement is zero at the equilibrium position, the bob still possesses maximum velocity due to the conversion of potential energy to kinetic energy. It is this exchange of energy that allows the pendulum to have the maximum velocity at the equilibrium position while having zero displacement.