A linear DC machine is an electromechanical system shown in the following figure. When the switch is closed the bar starts to move on the right side. 1. Determine the transfer function G (s) = X(s) VB (S)' where x(t) is position of the bar in m/s and v (t) is the applied DC voltage. It is important to mention that x(t) is positive on the right side and negative towards left side. The definition and values of model parameters are given as follows: (CLO1-PLO1[C3]) a. R = 0.12 is the resistance of the armature circuit; B = 0.5 T is the magnetic flux density (into the page); 1= 0.5 m and m = 2 kg are the length and mass of the bar, respectively; and K = 1 N/m and b = 2 Ns/m represent the stiffness of the bar and the damping coefficient representing friction between bar and the rails, respectively. b. The induced force acting on the bar is Find=ilB N and the back emf eind = v(t) Bl, where v(t) = x(t) is the velocity of the bar. VB t=0 R X X X eind X + Bar 1 X B F ind V Rails