A linear actuator is used in the system shown in Figure P8.10 to position a mass M. The actual position of the mass is measured by a slide wire resistor, and thus H{s) = 1.0. The amplifier gain is selected so that the steady-state error of the system is less than 1 % of the magnitude of the position reference R(s). The actuator has a field coil with a resistance Rf = 0.1 ft and Lf = 0.2 H. The mass of the load is 0.1 kg, and the friction is 0.2 N s/m. The spring constant is equal to 0.4 N/m. (a) Determine the gain K necessary to maintain a steady-state error for a step input less than 1 %.That is, Kp must be greater than 99. (b) Sketch the Bode diagram of the loop transfer function, L(s) = G(s)H(s). (c) Sketch the logarithmic magnitude versus phase angle curve for L(jco). (d) Sketch the Bode diagram for the closed-loop transfer function, Y(jco)/R(ju>). Determine Mpa>, a>r, and the bandwidth.