Physics of Trampolines

This coming Friday, I'm going to Skyzone with a bunch of my friends. If you've never been to Skyzone, an indoor trampoline park, you definitely should go. I've been thinking about the ways that trampolines work, and notice that they demonstrate an important physical concept: conservation of mechanical energy. When jumping on a trampoline, your weight and work done by your legs causes the elastic surface of the trampoline to stretch and it causes the springs attached to the trampoline to stretch.  The springs and surface of the trampoline eventually stretch until the velocity of the person is 0 m/s. This is the point at which the springs and surface are at their amplitude. Since spring potential energy equals 1/2 k x^2, the greater the amplitude or maximum displacement from equilibrium, the greater the spring potential energy in the system. Since mechanical energy is conserved, the spring potential energy when the springs and surface of the trampoline are at their amplitude must equal the gravitational potential energy when the person jumping is at their maximum height. Therefore, the more work that your legs do in stretching the surface and springs of the trampolines, the greater their amplitude will be, causing the spring potential energy to be greater, causing the maximum height that you reach to be greater.