Practice Problem: Mechanical System Modeling In many mechanical positioning systems there is flexibility between one part of the system and another. An example is shown in the figure below, where a force u is applied to the mass M, and another mass m is connected to it. The coupling between the objects is often modeled by a spring constant k with a damping coefficient b. a. Write the equations of motion governing this system. b. Find the transfer function between the control input, 1, and the output, y. c. Propose a disturbance that could influence the plant. m x k M b u