3.8 Consider a LTI system with transfer function Y (s) s2 +4 H(s) X (s) s(s + 1)2 + 1) (a) Determine if the system is BIBO stable or not. (b) Let the input be x(t) = cos(2t)u(t); find the response y(t) and the corresponding steady- state response. (c) Let the input be x(t) = sin(2t)u(t); find the response y(t) and the corresponding steady- state response. (d) Let the input be x(t) =u(t); find the response y(t) and the corresponding steady-state response. (e) Explain why the results above seem to contradict the result about stability. Answers: For x (t) = cos(2t)u(t), lim,→∞ y(t) = 0; if x(t) = u(t) there is no steady state.
3.8 Consider a LTI system with transfer function Y (s) s2 +4 H(s) X (s) s(s + 1)2 + 1) (a) Determine if the system is BIBO stable or not. (b) Let the input be x(t) = cos(2t)u(t); find the response y(t) and the corresponding steady- state response. (c) Let the input be x(t) = sin(2t)u(t); find the response y(t) and the corresponding steady- state response. (d) Let the input be x(t) =u(t); find the response y(t) and the corresponding steady-state response. (e) Explain why the results above seem to contradict the result about stability. Answers: For x (t) = cos(2t)u(t), lim,→∞ y(t) = 0; if x(t) = u(t) there is no steady state.
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Question
![3.8 Consider a LTI system with transfer function
Y (s)
s2 +4
H (s)
X (s)
s(s + 1)2 + 1)
(a) Determine if the system is BIBO stable or not.
(b) Let the input be x(t) = cos(2t)u(t); find the response y(t) and the corresponding steady-
state response.
(c) Let the input be x(t) = sin(2t)u(t); find the response y(t) and the corresponding steady-
state response.
(d) Let the input be x(t) =u(t); find the response y(t) and the corresponding steady-state
response.
(e) Explain why the results above seem to contradict the result about stability.
Answers: For x (t) = cos(2t)u(t), lim;→∞ y(t) = 0; if x (t) = u (t) there is no steady state.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F715ad422-c0c9-4bb1-9209-6734503c0d0c%2F544e4aad-90f3-4ebb-bf1a-088afba2a68e%2Frddt6ph_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.8 Consider a LTI system with transfer function
Y (s)
s2 +4
H (s)
X (s)
s(s + 1)2 + 1)
(a) Determine if the system is BIBO stable or not.
(b) Let the input be x(t) = cos(2t)u(t); find the response y(t) and the corresponding steady-
state response.
(c) Let the input be x(t) = sin(2t)u(t); find the response y(t) and the corresponding steady-
state response.
(d) Let the input be x(t) =u(t); find the response y(t) and the corresponding steady-state
response.
(e) Explain why the results above seem to contradict the result about stability.
Answers: For x (t) = cos(2t)u(t), lim;→∞ y(t) = 0; if x (t) = u (t) there is no steady state.
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