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1 results

  • Chapter Two - Mathematical Description of Oscillations

  • Johannes Falnes, Adi Kurniawan
  • Book:
    Ocean Waves and Oscillating Systems
    Published online:
    12 May 2020
    Print publication:
    28 May 2020, pp 6-45

  • 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.