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Damping characteristics of a fractional oscillator

Author

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  • Narahari Achar, B.N.
  • W. Hanneken, John
  • Clarke, T.

Abstract

A study of sinusoidally forced oscillations of a fractional oscillator shows that the system exhibits a rich variety of damping characteristics. While some aspects of the damping mimic the characteristic features of a damped harmonic oscillator, there are others, which do not find any parallel in the damped harmonic oscillator system. It is clearly demonstrated that the “free” and “forced” oscillations of a fractional oscillator are characterized by different damping parameters. While both depend on the fractional index α, the “free” oscillation damping depends on the “natural frequency”, ω0, of the oscillator, the “forced” oscillation damping depends in addition, on the “driving frequency”, ω. Furthermore, there is a different power-law tail associated with each of these cases.

Suggested Citation

  • Narahari Achar, B.N. & W. Hanneken, John & Clarke, T., 2004. "Damping characteristics of a fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 311-319.
    • Handle: RePEc:eee:phsmap:v:339:y:2004:i:3:p:311-319
    DOI: 10.1016/j.physa.2004.03.030
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    Citations

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    Cited by:

    1. Drozdov, A.D., 2007. "Fractional oscillator driven by a Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 237-245.
    2. Berman, Michael & Cederbaum, Lorenz S., 2018. "Fractional driven-damped oscillator and its general closed form exact solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 744-762.
    3. Lenzi, E.K. & Mendes, R.S. & Gonçalves, G. & Lenzi, M.K. & da Silva, L.R., 2006. "Fractional diffusion equation and Green function approach: Exact solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 215-226.

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