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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) +6¾y(t) + 13y(t) = ±x(t) + 2x(t). System 2: y(t) +6% 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? =

Consider the following ODEs modeling causal LTI systems at initial rest, with input x(t) and output y(t). System 1: y(t) +6¾y(t) + 13y(t) = ±x(t) + 2x(t). System 2: y(t) +6% 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? =

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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? =
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

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?
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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