Fourier Series Assignment

I looked up a Pogo Stick model name (Flybar 1200) online at [1]and found out some interesting data. For example the piston length for the this type of model is 7-18 inches. The longer you extend the piston the higher you will go. On average the ratio of height is 2*Piston length, although there are some individuals that surpass this statistic. The Pogo Stick can hold riders 120-250lb and in itself it weighs 21lb. It has a thrust capability of 1,200lb of force and a potential height of 5ft.I want to calculate what is the maximum height a rider that is 150lbs can go with the piston length being 18in, to maximize height.