In the following tmnslational mechanical system the input is f(t) and the output is /;he force in spring k 3 .
~ 1 ~I j=}~:~.---m----, 4---- u bl Translational Mechanical System

(a) Draw the free-body diagrams joT the mass m and the massless point A.

(b) Write down the system eqnations of motion

(c) Choose the minimum set of state variables for the system and develop the state-variable m.atri:r model (i.e. obtain A, B, C and D).