(a) Draw the free-body diagrams for the rotational mechanical system shown below (Figure 2.52).

(b) Explain why the state-variable vector should be chosen as

\[\mathbf{x}(t)=\left[\begin{array}{llll}\theta_{1} & \theta_{3} & \omega_{1} & \omega_{2}\end{array}ight]^{T}\]

(c) Express the dynamic equations in the State-Variable Matrix model (i.e. obtain \(A, B, C, D\) ) where the input is the applied torque \(T(t)\) and the output is the viscous frictional torque on disk \(J_{2}\).

Transcribed Image Text:

002 Tt) b Figure 2.52 Rotational mechanical system. 03 Negligible Inertia Fixed End 01 k