8. Determine the frequency at which the gain has unit magnitude and compute the phase angle at that frequency: a. = 1 rad/s,

8. Determine the frequency at which the gain has unit magnitude and compute the phase angle at that frequency:

a. ω = 1 rad/s, φ = −82°

b. ω = 1.26 rad/s, φ = −133°

c. ω = 1.26 rad/s, φ = 133°

d. ω = 4.2 rad/s, φ = −160°

Phase (deg) Magnitude (dB) 50 0 -50 -100 -90 -135 -180 10-2 50 0 -50 -100 Phase (deg) Magnitude (dB) 9 -90 -180 10-2 10- 10-1 10 10 Frequency (rad/s) (a) 10' 102 10' 10 Frequency (rad/s) (c) FIGURE 8.54 Bode plot selections. Magnitude (dB) Phase (deg) Phase (deg) Magnitude (dB) 100 50 0 -50 -100 -90 88.88 -135 -180 102 101 10 10' 10 103 20 0 -20 -40 -0 Frequency (rad/s) (b) -45 -90 10-2 101 10 101 102 Frequency (rad/s) (d)