Consider the system in the following diagram, where there is a viscous element B2, K1 is a translational element, and K2 is a rotational element. Let t(t) be the applied torque, x1 the displacement of M from rest, and u the angular displacement of the element J from rest (i.e., when the springs are neither stretched or compressed). The pulley has no inertia or friction, and the cable does not stretch.
(a) Write the differential equations that describe the system.
(b) Write the state variable equations that describe the system.
