A cycle can be described as a repeating process. It is a system
that has an initial state and goes through a process where the
final state is the same as the initial state. In the examples
of a bouncing ball and a swinging pendulum, gravitational potential
energy is converted into kinetic energy and back to gravitational
potential energy over and over in a repeating pattern.
For the ball, the initial state is when it is at the maximum height above the table. As it falls, its gravitational potential energy is converted into kinetic energy. When the ball hits the ground, its kinetic energy changes the shape of the ball, storing the energy as elastic potential energy.
When the ball bounces upward again, the elastic potential energy is released and converted back into kinetic energy. As the ball rises, its kinetic energy is gradually converted back into gravitational potential energy until the ball reaches the peak height where all its energy is in the form of gravitational potential again. This is the final state of the system. The ball repeats the cycle by falling back towards the ground.