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Chapter Two - Mathematical Description of Oscillations

Published online by Cambridge University Press:  12 May 2020

Johannes Falnes  and
Adi Kurniawan
Johannes Falnes
Affiliation:
NTNU, Norwegian University of Science and Technology, Trondheim
Adi Kurniawan
Affiliation:
University of Western Australia, Albany
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Summary

Chapter 2 starts by analysing free and forced oscillations in a simple mechanical system, and the method of complex representation of sinusoidal oscillation is introduced, including phasor diagram in the complex plane. Moreover, the concepts of active and reactive power for such a system are introduced. Then the method of state-space analysis is introduced and applied to a linear system. Further, the delta 'function' and other related distributions, as well as Fourier analysis, are introduced and applied to linear systems. Moreover, causal and noncausal systems are considered, as well as Kramers–Kronig relations and the Hilbert transform.

Keywords

quality factorphasoractivereactivestate-spacetime-invariantKramers–KronigcomplexresponselinearFourierharmonicoscillationpowermechanicalamplitudeimpulsecausalconvolutionimpedanceresonancedampingkineticpotentialreactance
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Chapter
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Ocean Waves and Oscillating Systems
Linear Interactions Including Wave-Energy Extraction
 , pp. 6 - 45
Publisher: Cambridge University Press
Print publication year: 2020

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