
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Transcribed Image Text:Consider the following ODEs modeling causal LTI systems at initial rest, with
input x(t) and output y(t).
System 1: y(t) +6dy(t) + 13y(t) =
d²
System 2: y(t)+6y(t) + 13y(t) =
x(t) + 2x(t).
x(t) — 2x(t).
(a) Is System 1 stable? Is it invertible with a causal stable inverse?
(b) Is System 2 stable? Is it invertible with a causal stable inverse?
(c) Find an explicit time domain expression for the response of System 1 to the input x(t)
5 sin(2t+1).
(d) Repeat (c) for System 2. How do the two responses differ?
=
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please do part d and check part c again. i dont think y(t) should be that long. is there anothere way to do it or simply it. again step by step soliutions and explain

Transcribed Image Text:Consider the following ODEs modeling causal LTI systems at initial rest, with
input x(t) and output y(t).
System 1: dy(t) +6ª y(t) + 13y(t) = ₫ x(t) + 2x(t).
System 2:
d2
y(t) +6ª y(t) + 13y(t) = x(t) — 2x(t).
(a) Is System 1 stable? Is it invertible with a causal stable inverse?
(b) Is System 2 stable? Is it invertible with a causal stable inverse?
(c) Find an explicit time domain expression for the response of System 1 to the input x(t)
5 sin(2t+1).
(d) Repeat (c) for System 2. How do the two responses differ?
Solution
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Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
please do part d and check part c again. i dont think y(t) should be that long. is there anothere way to do it or simply it. again step by step soliutions and explain

Transcribed Image Text:Consider the following ODEs modeling causal LTI systems at initial rest, with
input x(t) and output y(t).
System 1: dy(t) +6ª y(t) + 13y(t) = ₫ x(t) + 2x(t).
System 2:
d2
y(t) +6ª y(t) + 13y(t) = x(t) — 2x(t).
(a) Is System 1 stable? Is it invertible with a causal stable inverse?
(b) Is System 2 stable? Is it invertible with a causal stable inverse?
(c) Find an explicit time domain expression for the response of System 1 to the input x(t)
5 sin(2t+1).
(d) Repeat (c) for System 2. How do the two responses differ?
Solution
by Bartleby Expert
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