3. Given that-atL1eu(t) ←R{s} > R{−a}determine the inverse Laplace transform ofX(s)=s+a2(s+2)s27s+12"R{s} > −3

Answered: 3. Given that -at L 1 e u(t) ← R{s} >…

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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The inverse z-transform of F(z) is: 10z2 -42z z? –10z+21 F(z) = Select one: O a.f(k) = (3 × 3k) – (7 × 7') - O b. f(k) = (3 × 7k) + (7 × 3k) O c.f(k) = (3 × 3k) + (7 × 7k) O d. f(k) = (7 × 7k) – (3 × 3k)
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1 Note: Please do not handwritten.
Consider the second-order system: dx₁ dt = -ax₁, dx2 dt = -bx₁ - Cx₂ where a, b, c > 0. What can you say about the system if one of these functions is a Lyapunov function
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d-f
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Q3 From Topic: Z-Transform a) Determine the Z-Transform of the signal x(n) = p"u(n) + q"u(-n – 1) Draw all possible ROCS b) Determine the Z-Transform of the following finite duration signal x1(n) = {3, 7, 8, 0, 2, 1}
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* Q5/ Solve the following D.E. using Laplace transform: • y"- 4y' + 4y = t³e2t, y(0) = 0, y' (0) = 0 | п! • Complete the solution & notice that L{ t"eat} = (s-a)n+1 1 • Ans: y 20 t5 e2t
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Problem 3. The following information is known about an LTI system (a) The system is causal (b) When the input is x[n] 1/1 3 2 Then the z-transform of the output is n u[n] 3 (2)" u[-n-1], 1-z-2 (1-z-¹)(1-2z-¹)* Y(z) = (a) Find the z-transform of x[n] (b) What are the possible choices for the ROC of Y(z) (c) What are the possible choices for a linear constant-coefficient difference equation used to describe the system? (d) What are the possible choices for the impulse response of the system?

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3. Given that -at L 1 e u(t) ← R{s} > R{−a} determine the inverse Laplace transform of X(s) = s+a 2(s+2) s27s+12 " R{s} > −3