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Quality Factor of Forced Oscillations of a Linear Fractional Oscillator

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Abstract

Analytical formulas for the amplitude–frequency and phase–frequency characteristics, as well as forced oscillations, of a fractional oscillator have been derived using the harmonic balance method. It has been found that these characteristics depend on the dissipative properties of a medium—memory effects, which are described by fractional-order derivatives. It has been shown that fractional orders of derivatives influence the decay of the oscillatory process and are related to its Q factor. Analytical curves of forced oscillation characteristics for a linear fractional oscillator give the idea that fractional orders can be considered as control parameters for an oscillatory process in a dissipative medium.

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Funding

This study was supported by Presidential Grant no. MK-1152.2018.1.

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Authors and Affiliations

  1. Institute of Cosmophysical Research and Radiowave Propagation, Far East Branch, Russian Academy of Sciences, 684034, Paratunka, Kamchatka Krai, Russia

    R. I. Parovik

  2. Vitus Bering State University, 683032, Petropavlovsk-Kamchatskii, Kamchatka Krai, Russia

    R. I. Parovik

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  1. R. I. Parovik
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Correspondence to R. I. Parovik.

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Translated by V. Isaakyan

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Parovik, R.I. Quality Factor of Forced Oscillations of a Linear Fractional Oscillator. Tech. Phys. 65, 1015–1019 (2020). https://doi.org/10.1134/S1063784220070154

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