We generalize the previously considered cases of a harmonic oscillator subject to a random force (Brownian motion), or having random frequency, or random damping. We consider here a random mass which corresponds to an oscillator where the particles of the surrounding medium adhere to the oscillator for some (random) time after collision, thereby changing the oscillator mass. Such a model is appropriate to chemical and biological solutions as well as to some nano-technological devices. The first moment and stability conditions for white and dichotomous noise are analyzed.
J. Portman, M. Khasin, S. W. Shaw and M. I. Dykman, “The Spectrum of an Oscillator with Fluctuating Mass and Nanomechanical Mass Sensing,” Bulletin of the American Physical Society, March Meeting 2010, Vol. 55, No. 2, Portland, 15-19 March 2010, Abstract V14.00010.
Y. Jia, X.-P. Zheng, X.-M. Hu and J.-R. Li, “Effect of Colored Noise in Stochastic Resonance in a Bistable System Subject to Multiplicative and Additive Noise,” Physical Review E, Vol. 63, 2001, p. 031107.