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4. Consider the differential equation y(t) + 4y(t) + 5 y(t) + 2y(t) = 4x(t) + x(t). (a) Find the frequency response of this LTI system. (b) Find the impulse response of this system. (c) Find the output when the input is 10e-4u(t)

4. Consider the differential equation y(t) + 4y(t) + 5 y(t) + 2y(t) = 4x(t) + x(t). (a) Find the frequency response of this LTI system. (b) Find the impulse response of this system. (c) Find the output when the input is 10e-4u(t)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Certainly! Here is the transcription for educational purposes: --- Consider the differential equation \[ \frac{d^3}{dt^3}y(t) + 4\frac{d^2}{dt^2}y(t) + 5\frac{d}{dt}y(t) + 2y(t) = 4x(t) + \frac{d}{dt}x(t). \] (a) Find the frequency response of this LTI system. (b) Find the impulse response of this system. (c) Find the output when the input is \( 10e^{-4t}u(t) \). --- This transcription is suitable for an educational website discussing topics related to differential equations and Linear Time-Invariant (LTI) systems.
Transcribed Image Text:Certainly! Here is the transcription for educational purposes: --- Consider the differential equation \[ \frac{d^3}{dt^3}y(t) + 4\frac{d^2}{dt^2}y(t) + 5\frac{d}{dt}y(t) + 2y(t) = 4x(t) + \frac{d}{dt}x(t). \] (a) Find the frequency response of this LTI system. (b) Find the impulse response of this system. (c) Find the output when the input is \( 10e^{-4t}u(t) \). --- This transcription is suitable for an educational website discussing topics related to differential equations and Linear Time-Invariant (LTI) systems.
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