In a simple pendulum, the velocity of the pendulum ball reaches 0 at the maximum amplitude because of the conservation of mechanical energy and the nature of simple harmonic motion.
When a pendulum ball swings, it moves between two extreme points, the highest point (maximum amplitude) and the lowest point (equilibrium position). As it swings, it undergoes simple harmonic motion, where its energy continuously oscillates between potential energy and kinetic energy.
At the equilibrium position (lowest point), the pendulum ball has its maximum kinetic energy but zero potential energy because it is moving with maximum speed and is at the lowest height. As it swings upward, it slows down due to the opposing force of gravity, and its kinetic energy is converted back into potential energy as it gains height.
At the maximum amplitude (highest point), the pendulum ball momentarily comes to a stop. This occurs because, at the highest point, the pendulum's kinetic energy is entirely converted into potential energy. Since it momentarily stops, its velocity at this point is 0.
As the pendulum ball swings back downward, the potential energy is converted back into kinetic energy, causing the ball to accelerate and gain speed as it approaches the equilibrium position again. The process repeats, and the ball swings back and forth, with its velocity continually changing throughout the motion.
This behavior is a characteristic of simple harmonic motion, where the restoring force (in this case, gravity) is proportional to the displacement from the equilibrium position and acts in the opposite direction, causing the object to oscillate around the equilibrium. At the maximum amplitude, the displacement is maximum, and the restoring force is at its strongest, momentarily bringing the object to rest before it reverses direction.