In the following mechanical system the input is a force f(t)

and the output is the spting force in k2.

(a) Draw the fret-body diagrams for the mass Tn an.d for /.he massless point A.

(b) WTite down the eqv.ations of motion.

(c) Choose the minimum number of state variables jirr the system and de'l'dop the state-variable matrix model (i.e. obtain A,

(d) If the dashpot b2 is Temoved show that 1 X3 k3 [(k2 + k3)X2- k2x1].
Choose a new set of independent state variables for this new system and develop the state-variable matTi:r model (i.e. obtain A, B, C, D).