Why does a diving bounce up and down after the diver jumps off its surface?
When left alone, the diving board settles down to its equilibrium shape and position — arrangement at which all of its parts are experiencing zero net force and are therefore not accelerating. If the board is disturbed from that arrangement and released, it will vibrate back and forth about that equilibrium arrangement until it settles down again.
When the diver leaves the diving board, the board is usually far from its equilibrium arrangement and its parts are usually moving as well. It consequently vibrates back and forth. Whenever it is above the equilibrium arrangement, the springiness of the board, assisted slightly by gravity, causes its parts to experience downward net forces and those parts accelerate downward. If the board was rising, it slows to a stop and then begins to descend toward the equilibrium. Whenever the board is below the equilibrium arrangement, its springiness, opposed slight by gravity, causes its parts to experience upward net forces and those parts accelerate upward. If the board was descending, it slows to a stop and then begins to rise toward equilibrium.
So whenever the board is away from equilibrium, it is accelerating toward that equilibrium and will soon be moving toward equilibrium. When it reaches equilibrium, however, it will be moving and will thus coast through equilibrium and overshoot. That’s why it bounces up and down — it keeps coasting through equilibrium, turning around, heading back toward equilibrium, and coasting through again. But with each bounce, the board wastes some of its energy as thermal energy via internal friction and air resistance. Its bounces get weaker and weaker until it eventually settles at equilibrium and stops moving altogether.