On the brownian motion of a frequencymodulated oscillator
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The Langevin equations for a harmonically bound particle, where the force constant is a given function of time, is solved. The mean and mean-square properties of the solution are determined. The analysis is then specialized to the case of a force constant periodic in time. It is shown that the mean fluctuations remain bounded in time precisely when the mean motion is stable (remains bounded).
Key wordsLangevin equations Brownian motion fluctuations Hill's equation
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