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PE=(1/2)kx^2
The potential energy stored in a spring: "x" is how much the spring stretches, and "k" is the spring constant. Hooke's law goes along with this: F=kx. The force of the spring is the constant multiplied by the change in the spring length. This demonstrates Newton's third law; every action has an equal and opposite reaction. When the springs are stretched by the person, they have to compress again, making the person jump higher as the trampoline returns to its original position. 

Because of gravity, larger masses allow the spring to be stretched out more. This can be shown by the equation F=ma, which is Newton's second law of motion. "F" is the force of gravity, "m" is mass, and "a" here is also g, acceleration due to gravity. So when mass increases, so does the force of gravity. This means the object/person is being pulled down harder by gravity. This stretches the springs of the trampoline more, creating a higher spring potential energy. But the mass is usually too heavy for the spring to move you if you just stand there, which is why you don't move unless you start jumping first.

Smaller kids usually jump higher than adults, even though they have a lower potential energy due to gravity, because the trampoline can more easily spring them back up, since they are being pulled down by gravity slightly less. 

This is all a great example of Newton's first law: objects in mot