The input x(t) and the output y(t) of a nonlinear system are related through the following differential equation y(t) = x 2 dx dt + 2x Prove that the describing function of this system can be given by √ A6ω2 16 + 4A2 e jtan−1( A 2ω 8 )

The input x(t) and the output y(t) of a nonlinear system are related through the following differential equation y(t) = x 2 dx dt + 2x Prove that the describing function of this system can be given by √ A6ω2 16 + 4A2 e jtan−1( A 2ω 8 )

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 7RE: Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.

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Question

The input x(t) and the output y(t) of a nonlinear system are related
through the following differential equation
y(t) = x
2
dx
dt + 2x
Prove that the describing function of this system can be given by
√
A6ω2
16 + 4A2 e
jtan−1(
A
2ω
8
)

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