In the following rotational mechanical system there is a driving torq11e T(t) exeTted on disk J 1 and a load torque TL(t) e:rerted on disk J2 . Both the applied torque T(t) and the load torque TL(t) aTe considered as inputs and the ou.tput is the angular velocity w3 ( t).

(a) Draw the free-body diagrams for the system.

(b) Explain why the vector of state variables can be chosen as

(c) Express the dynamic equations in state-variable matrix form (i.e.
obtain A, B, C, D).

(b) Use the s-operator method to express the dynamic equations in the form of an ·input-ov.tput differential equation.