Response of Van Der Pol’s Oscillator to Random Excitation

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Abstract
This paper considers the response of Van der Pol’s oscillator to random excitation. It is shown that the output of the oscillator consists of a periodic term, plus a narrow band noise term centered at the natural frequency of the oscillator. The root-mean-square amplitude of this noise term is shown to be proportional to the square root of the spectral density of the excitation, and inversely proportional to the amplitude of self-oscillation.

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