For the second-order systems below, (1) plot the roots on the s-plane, (2) characterize the system's damping, and (3) sketch the free response of the system, assuming the system has initial conditions x(0) = 1 and x(0) = 0. a. b. C. d. G(s) U(s) G(s) U(s) = 25 s²+25 G(s) 12 U(s) s²+s+12 12 s²+12s-12 = G(s) 12 U(s) s²+12s+12

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5) For the second-order systems below, (1) plot the roots on the s-plane, (2) characterize the
system's damping, and (3) sketch the free response of the system, assuming the system has
initial conditions x(0) = 1 and x(0) = 0.
G(s)
25
U(s) s²+25
a.
b.
C.
d.
G(s)
U(S)
G(s)
U(s)
=
=
=
12
s²+12s-12
=
12
s²+s+12
G(s)
12
U(s) s²+12+12
Transcribed Image Text:5) For the second-order systems below, (1) plot the roots on the s-plane, (2) characterize the system's damping, and (3) sketch the free response of the system, assuming the system has initial conditions x(0) = 1 and x(0) = 0. G(s) 25 U(s) s²+25 a. b. C. d. G(s) U(S) G(s) U(s) = = = 12 s²+12s-12 = 12 s²+s+12 G(s) 12 U(s) s²+12+12
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