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another_someone is right about the resonance thing, of course and the two resonant frequencies would need to be equal - or at least, harmonically related.As usual, I will bring energy into my argument.Each time you bounce, you put some energy into the system with your leg muscles. The height you reach depends on the kinetic energy with which you start each upward trip. (Potential Energy Gained = kinetic energy lost)When you return, you have alomst the same KE as when you left (less the friction losses) The springs and fabric stretch and store most of your KE plus the energy from your legs, returning it on the way up. The limit to your height reached will be when your legs just supply enough energy to make up for what you lost due to friction each bounce.Your space hopper would probably introduce MORE loss into the system so you would probably not get as high, in fact. You could discuss this with the doctor in casualty, when you get there!A more efficient system would get you much higher - suspending yourself on a long spring and carrying some heavy masses would work well, once you had found the right (resonant) frequency.One of the problems in any such system is 'matching' the energy input to the system. There will be an optimum length of leg and body mass for getting the best height on a particular trampoline. A mouse, for instance, wouldn't get anywhere on a human trampoline but could jump quite high (with practice) on a specially designed one. Though, whether he would be bothered to, is another matter.Btw, your achilles tendon (and a kangaroo's even more so) stores a significant amount of energy whist you are running. You spring higher than you would with a non resilient tendon.
I thought someone would bring energy in to the problem  .So, how about those balls made of rubber bands that kids, and bored adults make. Do they gain or lose energy when bounced?