Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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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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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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

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?
expand button
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?
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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

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?
expand button
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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by Bartleby Expert
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