Consider the linearized dynamics of an inverted pendulum with friction 10 P(s): 8-98-10 You will determine if the closed-loop system is stable or not for two different controllers using Nyquist plots and the Nyquist stability criterion. Please answer the following questions. (a) What are the poles and zeros of the plant? How many unstable poles are there? (b) Sketch the Bode plot for L(s) when C(s) = 10 and s = jw. (c) Sketch the Nyquist plot for L(s) when C(s) = 10 and s = jw. State whether the closed-loop system is stable or unstable using the Nyquist stability criterion. (d) Can the system be stabilized with any proportional controller with a positive feedback gain? Justify your reasoning. (e) Sketch the Bode plot for L(s) when C(s) = 2.1s + 3 and s = jw. (f) Sketch the Nyquist plot for L(s) when C(s) = 2.1s+3 and s = jw. State whether the closed-loop system is stable or unstable using the Nyquist stability criterion.