Only for genius people: jumping stilts on a trampoline.

[Cyrus]

m \ddot{x} = -m g + b x - k x where +ve x is upward, b is the spring constant of the trampoline, and k is the spring constant of the stilts.

Im afraid its not that simple. The trampoline will not be an ideal spring, but rather some sort of a membrane. It will take the shape of a "well" so to speak, and I doubt the spring constant will be directly linear as you propose, but it could be very nearly the same.