What is the correlation in spring dynamics involving kinetic and potential energy?

The correlation between kinetic energy (KE) and potential energy (PE) in the context of spring dynamics is best illustrated by the relationship that occurs when a spring is compressed or stretched. When an object compresses a spring, it does work on the spring, which converts the kinetic energy of the object into potential energy stored in the spring. As the spring is compressed, the potential energy in the spring increases, and this energy is directly related to the amount of compression according to Hooke's law, which states that the force exerted by a spring is proportional to its displacement.

At full compression, the object's kinetic energy is at its maximum just before the point of maximum compression, and it is 0 as the spring reaches its maximum compression. At that point, all the kinetic energy has been transformed into the potential energy of the spring. As the spring decompresses, the potential energy converts back into kinetic energy, thereby demonstrating the conservation of mechanical energy in the system. This connection conveys the dynamic exchange of energy between kinetic and potential forms during the motion of objects interacting with springs.

This reasoning confirms why the correct answer involves the kinetic energy of the object equaling the potential energy of the spring being compressed, illustrating the energy transfer during the interaction.