USe MA TLAI3" s frequency-response plotting A second-order system's transfer function can he represented using a natural frequency Wn, a damping ratio ;;, and a DC gam K

Gts) = N(s)/D(S)

Nts) = Kw":

(a) Make a single Bode plot for a system With a DC gam K = I and a natural frequency w" = I rad/s, for the following damping ratios::;' = 0 I. (lA. () 7. I. I 3, I 6. Use the MA TLAB function bode to accomplish this. For the underdamped systems. measure the frequency of the resonance peak from the plot and confirm that It IS the same as the damped natural frequency WJ Turn III your fullv labeled plot. as well as the rn-file that you used to make the plot

(h) Make a single Bode plot for a critically damped system With natural frequency Wn = I rad/s. forthe following DC gams: K = 0 I. 0 5. I. 5. I() Verifv that the DC gains (Ill dls) are what vou expect. Turn III Your tullv labeled plot. as well as the rn-file that you used to make the plot.

(c) For a system with Wn = I rad/s. K = I. and t; = 0.4. measure the magnitude M and phase «p asaccuratelv as YOU can for your plot at w = 0 5. 0 8. 3, and 1(1tad/sec. Then calculate the values of1\1and «p at those same' frequencies and compare your answers to the ones you obtamed graphically: they should he close.