We study the dynamics of an oscillator with a friction term being quadratic in the time derivative of the amplitude Psi , Psi - gamma Psi 2 +k Psi =0. Using methods of analytical and non-linear mechanics, a classification of the dynamics of the system is presented. The range of existence of periodic solutions and their frequencies are also determined.
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S. J. Linz (1995) studied this question.
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