Consider the mechanical system shown below, where the input is a displacement \(y_{2}(t)\), and the output is the force in spring \(k_{3}\).

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

(b) Obtain the equations of motion.

(c) Choose a minimum set of variables for the system and justify the choice.

(d) Derive the State-Variable Matrix model by expressing the equations of motion in a StateVariable Matrix model (i.e. obtain A, B, C, D).

k2 bi mi bz no friction k3 000 y2(t) m2