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A dynamic system with a transfer function S G(s) = ; 3s +1 receives an input u(t) = sin ot where the frequency @ varies over operation. (a) Write an expression for the steady state output y(t) in terms of the frequency parameter w valid for any such sinusoidal input. (b) Systems of this type are often called practical differentiators because their output is ap- proximately the derivative of the input signal. Using the expression you obtained for the output, explain in 5 sentences or fewer why this definition works. hint: the trigonometric identities cos (-0) = cos (0) and cos (0) = sin (90° – 0) may be helpful. (c) What is the behavior of the transfer function at high frequencies?

A dynamic system with a transfer function S G(s) = ; 3s +1 receives an input u(t) = sin ot where the frequency @ varies over operation. (a) Write an expression for the steady state output y(t) in terms of the frequency parameter w valid for any such sinusoidal input. (b) Systems of this type are often called practical differentiators because their output is ap- proximately the derivative of the input signal. Using the expression you obtained for the output, explain in 5 sentences or fewer why this definition works. hint: the trigonometric identities cos (-0) = cos (0) and cos (0) = sin (90° – 0) may be helpful. (c) What is the behavior of the transfer function at high frequencies?

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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A dynamic system with a transfer function S G(s) = ; 3s +1 receives an input u(t) = sin @t where the frequency o varies over operation. (a) Write an expression for the steady state output y(t) in terms of the frequency parameter o valid for any such sinusoidal input. (b) Systems of this type are often called practical differentiators because their output is ap- proximately the derivative of the input signal. Using the expression you obtained for the output, explain in 5 sentences or fewer why this definition works. hint: the trigonometric identities cos (-0) = cos (0) and cos (0) = sin (90° – 0) may be helpful. (c) What is the behavior of the transfer function at high frequencies?
Transcribed Image Text:A dynamic system with a transfer function S G(s) = ; 3s +1 receives an input u(t) = sin @t where the frequency o varies over operation. (a) Write an expression for the steady state output y(t) in terms of the frequency parameter o valid for any such sinusoidal input. (b) Systems of this type are often called practical differentiators because their output is ap- proximately the derivative of the input signal. Using the expression you obtained for the output, explain in 5 sentences or fewer why this definition works. hint: the trigonometric identities cos (-0) = cos (0) and cos (0) = sin (90° – 0) may be helpful. (c) What is the behavior of the transfer function at high frequencies?
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