Consider the child at the top of her flight, when she has maximum gravitational potential energy. As she falls, this gravitational potential energy is transformed into kinetic energy. As the child hits the ground, this KE and gravitational PE are transformed into elastic (spring) potential energy, as the spring compresses. At the very bottom, her KE and gravitational PE are zero, and all of the system’s energy is in the form of spring PE.
Work Step by Step
After each bounce, the process reverses: the spring expands, transforming its stored energy back to kinetic and gravitational potential energy. As she rises, she has less KE and more gravitational PE. At the top, the cycle repeats.