Consider the mechanical system shown in Figure B$3.$ m is the mass of the body. b is

damping coefficient. k is stiffness of spring. F is the applied force.

Figure B$3$

$($a$)$ Consider the applied force F is the input and the velocity of the body of mass m

is the output of the system. Write the state$-$space equations for the system.

$[40\%]$

$($b$)$ What is the transfer matrix of the system?

$[20\%]$

$($c$)$ What is the state feedback controller? Please design a state feedback

controller to place the close loop poles to better values