A second-order mechanical microsystem is formed of a shuttle mass and a serpentine spring attached to an anchor. The microsystem, whose mechanical properties are not known precisely, vibrates in a gas...

A second-order mechanical microsystem is formed of a shuttle mass and a serpentine spring attached to an anchor. The microsystem, whose mechanical properties are not known precisely, vibrates in a gas with unknown damping properties. This system acts as a plant in a unity-feedback system, which also contains a proportional controller (actuator). Applying a unit step input to the control system, it is obtained experimentally that the rise time is xr = 0.002 s whereas the settling time is xs = 0.3 s. Identify the closed-loop transfer function of this system.