Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Periodical Damping Ratio of a Controlled Dynamical System with
  Parametric Resonances   This report provides an interpretation on the periodically varying damping
ratio of a dynamical system with direct control of oscillation or vibration
damping. The principal parametric resonance of the system and a new type of
parametric resonance, named "zero-th order" parametric resonance, are
investigated by using the method of multiple scales to find approximate,
analytical solutions of the system, which provide an interpretation on such
damping variations.

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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph