An electric motor is sometimes used to move the spool valve of a hydraulic motor. In Figure

Question:

An electric motor is sometimes used to move the spool valve of a hydraulic motor. In Figure the force f is due to electric motor acting through a rack-and-pinion gear. Develop a model of the system with the load displacement y as the output and the force f as the input. Consider two cases:
(a) m1 = 0
(b) m1 ‰ 0.