Consider the following LTI system: The differential equation given is \((D^2 + 7D + 6)y(t) = x(t)\), with the initial conditions \(y(0) = \dot{y}(0) = 1\), and the input \(x(t) = e^{-3t}u(t)\).Use s-domain techniques to determine:(a) the impulse response,(b) the zero-input response,(c) the zero-state response.

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Answered: (D°+7D+6)y(t)=x(t) , with y(0)=y(0)=1 ,…

(D°+7D+6)y(t)=x(t) , with y(0)=y(0)=1 , and x(t)=etu(t) . Use s-domain techniques to determine (a) the impulse response (b) the zero-input response (c) the zero-state response

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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Question

Consider the following LTI system:

The differential equation given is \((D^2 + 7D + 6)y(t) = x(t)\), with the initial conditions \(y(0) = \dot{y}(0) = 1\), and the input \(x(t) = e^{-3t}u(t)\).

Use s-domain techniques to determine:
(a) the impulse response,
(b) the zero-input response,
(c) the zero-state response.

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