# Non-linear force to linear force equation

by jimgram
Tags: equation, force, linear, nonlinear
 P: 92 Your solution works where both f and f' are known. If you know f' and f you can find x, and then f' = f*x/(C-x). But you need x to find f' and you need f' to find x. I believe I have found a solution: It is required that the distance traveled for f and f' be equal. Work is equal to force times distance, so if distance is equal and f is a function of n, then the work done by f is $\int f(n) dn$. This yields a constant value for the area under the curve of f(n). So now the ratio(n) (which is x/x') is equal to($\int f(n) dn$)/f(n)*n. Then f'(n) is equal to f(n)*ratio(n), and f'(n) is constant. The net result is that the ratio varies as f(n) varies to maintain a constant counterbalance force f'.