Consider the following mechanical system.

~-1

~I f(t) ,-------,

-~

Is Translational Mechanical System The forces exerted by the springs an zero when x1 = :r:2 = X3 = 0. The input force is j(t) and the absolute displacements of m 1 , m2 and m3 arc

:r1, xz and X3, respectively

(a) Draw the free-body diagmrns of the system.

(b) Obtain the syst.em dynamic equations of motion.

(c) Choose a suitable vector of state variables and justify your choice.

(d) Express the dynamic equations in the state-1mriable matrix form (A, B, C, D), where the output is the spring force in