In the following problems we use the inverse Laplace transform and the relation between inputand output of LTI systems.(a) The Laplace transform of the output of a system is(s +2)² + 2.+-2sY1 (s)=s2 +1(s +2)3find y1 (t), assume it is causal.(b) The Laplace transform of the output y2(t) of a second-order system is-s2 – s+1s (s² + 3s + 2)'Y2(s) =2332CHAPTER 3 THE LAPLACE TRANSFORMIf the input of this system is x2(t) =u(t), find the ordinary differential equation that represents the system and the corresponding initial conditions y2(0) and dy2(0)/dt.(c) The Laplace transform of the output y(t) of a system is%3D1Y (s) =s(s +1)2 +4)*Assume y(t) to be causal. Find the steady-state response yss (t), and the transient y; (t).(b) y2(0) = -1dy2(0)/dt =2; (c) transient y; (t) =[-(1/5)e¬ cos(2t) – (1/10)e¬ sin(2t)]u(t).Answer:(a) yı(t) = sin(t – 2)u(t – 2) +e¯2ªu(t) +t²e-2ª u (tanc

In order to solve differential equations, the Laplace transform is employed. It is widely accepted…

In the following problems we use the inverse Laplace transform and the relation between input and output of LTI systems. (a) The Laplace transform of the output of a system is (s +2)² + 2 (s +2)³ e-2s Y1 (s) = s2 +1 find yı (t), assume it is causal. (b) The Laplace transform of the output y2(t) of a second-order system is -s2 – s+1 s (s2 + 3s + 2) Y2(s)=

In the following problems we use the inverse Laplace transform and the relation between input and output of LTI systems. (a) The Laplace transform of the output of a system is (s +2)² + 2 (s +2)³ e-2s Y1 (s) = s2 +1 find yı (t), assume it is causal. (b) The Laplace transform of the output y2(t) of a second-order system is -s2 – s+1 s (s2 + 3s + 2) Y2(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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1. What is the Transfer Function of this Differential Equation? 2. Find the solution to the dierential equation in the time domain assuming y (t) = Aest (you are not allowed to use Laplace transforms). Use the initial conditions y (0) = 1/6 , y'(0) = 5, with f (t) = u(t).
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