Question

how oscillation occurs in stable equillibrium

Answer 1

For a swing or pendulum, maximum displacement occurs when the object is at its highest point on either side of the stable equilibrium position. For example, maximum displacement in a spring occurs when the spring reaches the furthest point of being either stretched or compressed.

Answer 2

An oscillation is a particular kind of motion in which an object repeats the same movement over and over. It is easy to see that a child on a swing and the pendulum on a grandfather clock both oscillate when they move back and forth along an arc.