Problem 2. (30 points) Consider the plant with transfer function G(s) = 1 (s+1)(s+2) 1) Sketch the Bode plot of G(s) (for K = 1). Explain what rules you used to plot it. 2) Find a value of K such that for the Bode plot of KG(s) the crossover frequency becomes Wc = 3. 3) Sketch the Nyquist plot based on the Bode plots. Determine the range of K for which the system is stable. Consider both positive and negative values of K. R K G(s) Y Figure 2: Control system in Problem 2.