November 14, 1998
What is potential energy? Imagine yourself jumping on a trampoline. (You and the trampoline are the system.) You are stop at the bottom of your motion and the trampoline is stretched (deflected) downward. At this point the trampoline has the vast majority of the energy and it is potential energy. You only have a small amount which comes from you being off the ground a few feet. As the trampoline begins to push you upward and give you velocity, it is starting to convert its potential energy to you. The instant you leave contact with the trampoline, it has given over all its energy to you and you have both kenetic energy and potential energy. The kenetic energy is associated with your speed and the potential energy is associated with your height. As you rise into the air you are slowing down which is the conversion of your kenetic energy to potential energy. At the top of you jump when you are stop, all your kenetic energy is gone. It has been converted to potential energy and neglecting friction this is the same amount of potential energy the trampoline and you had at the bottom of your jump. As you begin to accelerate downward you start converting your potential energy to kenetic energy again. When you touch the trampoline, it begins to store potential energy as it stretches and slows you down. When you come to a stop at the bottom of your jump the distributions of potential energy between you and trampoline are the same as the start of this discussion.
I have used the trampoline analogy because it similar to a spring. When a spring or solid body is deflected, work has been done on it and this work is stored as potential energy. If the spring has not been permanently deformed then when it is released it will returns to it original shape and give up the stored potential energy.