The input x(t) and the output y(t) of a nonlinear system are related through the following differential equation y(t) = x2dx/dt + 2x Prove that the describing function of this system can be given by √A6ω2 / 16 + 4A2 e jtan−1(A2ω/ 8)

The input x(t) and the output y(t) of a nonlinear system are related through the following differential equation y(t) = x2dx/dt + 2x Prove that the describing function of this system can be given by √A6ω2 / 16 + 4A2 e jtan−1(A2ω/ 8)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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) = x²dx/dt + 2x
Prove that the describing function of this system can be given by
√A⁶ω² / 16 + 4A² e jtan−1(A²ω/ 8)

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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