Abstract
This chapter is devoted to the analysis of the single degree-of-freedom oscillator, with and without viscous damping, in the time domain: Impulse response and convolution integral, and in the frequency domain: harmonic response, dynamic amplification, quality factor. The chapter also reviews various representations of the frequency response function: Bode plots and Nyquist plot. The Beat phenomenon resulting from an excitation close to the resonance frequency is analyzed. Finally, the state space forms of the equation of motion are introduced. The chapter ends with a set of problems.
La vraie science est une ignorance qui se sait. Montaigne, Essais (1572-1588)
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- 1.
The second integral is readily obtained by the change of variables \(u=t-\tau \).
- 2.
The Fourier transform is one of the magic tools of mathematics which is used in almost all fields of physics; see (Papoulis 1962) for a clear exposition, although the book was written before the Fast Fourier Transform.
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Preumont, A. (2013). Single Degree-of-Freedom Linear Oscillator. In: Twelve Lectures on Structural Dynamics. Solid Mechanics and Its Applications, vol 198. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6383-8_1
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DOI: https://doi.org/10.1007/978-94-007-6383-8_1
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