The transfer function of a linear system is defined as the

Chapter 7, Problem 29E

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The transfer function of a linear system is defined as the ratio of the Laplace transform of the output function y(t) to the Laplace transform of the input function g(t), when all initial conditions are zero. If a linear system is governed by the differential equation

\(y^{\prime \prime}(t)+6 y^{\prime}(t)+10 y(t)=g(t), t>0\)

use the linearity property of the Laplace transform and Theorem 5 on the Laplace transform of higher order derivatives to determine the transfer function \(H(s)=Y(s) / G(s)\) for this system.

Equation transcription:

Text transcription:

y^{prime prime}(t)+6 y^{prime}(t)+10 y(t)=g(t), t>0

H(s)=Y(s) / G(s)

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