Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 21

It is helpful to investigate the ongoing processes from the energy perspective. For an undamped system cv=0 that oscillates with u(t)=u^cos⁡(ω0t) and absence of external forces the energy remains constant. The energy is the sum of kinetic E_kin and potential energy E_pot

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and is constant, but spring and mass exchange energy twice over one period T₀.

Figure 1.8 Kinetic and potential energy of the harmonic oscillator. Source: Alexander Peiffer.

As energy quantities are not always constant, this motivates the definition of time average values. average ! time We introduce the mean-square (ms) and root-mean-square (rms) value for the time average for an arbitrary signal x(t). The mean-square value over a time T is

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In the following ⟨⋅⟩T=1T∫0T⋅dt denotes a time average. If the signal is harmonic with u(t)=u^cos⁡(ω0t) then

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