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Problem 7. (B07) For the following systems, determine (i) if they are linear and (ii) if they are Time-Invariant (TI). Ti {x(t)} = y(t), s.t. D°y(t) + ty(t) = ¤(t) T2 {r(t)} = y(t), s.t. Dy(t – 1) + 3y(t) = ¤(t) T3 {r(t)} = y(t), s.t. D°y(t) – 2y²(t) = x(t) (За) (3b) (3c)

Problem 7. (B07) For the following systems, determine (i) if they are linear and (ii) if they are Time-Invariant (TI). Ti {x(t)} = y(t), s.t. D°y(t) + ty(t) = ¤(t) T2 {r(t)} = y(t), s.t. Dy(t – 1) + 3y(t) = ¤(t) T3 {r(t)} = y(t), s.t. D°y(t) – 2y²(t) = x(t) (За) (3b) (3c)

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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Problem 7. (B07) For the following systems, determine (i) if they are linear and (ii) if they are Time-Invariant (TI). Ti {x(t)} = y(t), s.t. D²y(t) + t²y(t) = x(t) (За) (3Ь) T2 {x(t)} = y(t), s.t. Dy(t – 1) + 3y(t) = ¤(t) T3 {x(t)} = y(t), s.t. D°y(t) – 2y²(t) = #(t) T4 {x(t)} = y(t), s.t. Dy(t) + y(t) = x²(t) T; {x(t)} = y(t), s.t. Dy(t) – 5y(t) = D¤(t) – 3x(t) (Зс) (3d) (3e) Hint: y(t) = L{x(t)} for this system means that the pair of signals (x, y) satisfies the given Ordinary Differential Equation (ODE). To show that L is homogenous, you need to show that the pair of amplitude-scaled signals (ax, ay) for any a e C satisfies the same ODE as the pair (x, y). Use a similar rationale for the other two properties.
Transcribed Image Text:Problem 7. (B07) For the following systems, determine (i) if they are linear and (ii) if they are Time-Invariant (TI). Ti {x(t)} = y(t), s.t. D²y(t) + t²y(t) = x(t) (За) (3Ь) T2 {x(t)} = y(t), s.t. Dy(t – 1) + 3y(t) = ¤(t) T3 {x(t)} = y(t), s.t. D°y(t) – 2y²(t) = #(t) T4 {x(t)} = y(t), s.t. Dy(t) + y(t) = x²(t) T; {x(t)} = y(t), s.t. Dy(t) – 5y(t) = D¤(t) – 3x(t) (Зс) (3d) (3e) Hint: y(t) = L{x(t)} for this system means that the pair of signals (x, y) satisfies the given Ordinary Differential Equation (ODE). To show that L is homogenous, you need to show that the pair of amplitude-scaled signals (ax, ay) for any a e C satisfies the same ODE as the pair (x, y). Use a similar rationale for the other two properties.
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