b) Consider a system defined by the ordinary differential equation d²y(t) dy(t) +5 dt² +4y(t) = 4- dt du(t) dt +16u(t) The initial conditions are defined as y(0) = 1 and y'(0) = 2. (i) Obtain the zero-input response of the system. Obtain the characteristic polynomial and the modes. (ii) Obtain the transfer function G(s) = Y(s)/U(s) of the system. (iii) Based on your result for the previous question [Question 3b)-(ii)], obtain the bandwidth of the system described by G(s).

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b) Consider a system defined by the ordinary differential equation
d²y(t) dy(t)
+5
dt²
+4y(t) = 4-
dt
du(t)
dt
+16u(t)
The initial conditions are defined as y(0) = 1 and y'(0) = 2.
(i) Obtain the zero-input response of the system. Obtain the
characteristic polynomial and the modes.
(ii) Obtain the transfer function G(s) = Y(s)/U(s) of the system.
(iii) Based on your result for the previous question [Question 3b)-(ii)],
obtain the bandwidth of the system described by G(s).
Transcribed Image Text:b) Consider a system defined by the ordinary differential equation d²y(t) dy(t) +5 dt² +4y(t) = 4- dt du(t) dt +16u(t) The initial conditions are defined as y(0) = 1 and y'(0) = 2. (i) Obtain the zero-input response of the system. Obtain the characteristic polynomial and the modes. (ii) Obtain the transfer function G(s) = Y(s)/U(s) of the system. (iii) Based on your result for the previous question [Question 3b)-(ii)], obtain the bandwidth of the system described by G(s).
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