Abstract
Using a simple matrix method, we have obtained exact second-order equilibrium moments for a linearly damped harmonic oscillator with a fluctuating frequency ω(t) and driven by a fluctuating forcef(t). We have assumed each of the fluctuating quantities to be delta-correlated. We demonstrate that the final answers are identical whetherf(t) and ω(t) are statistically independent or delta-correlated. We have also established the region of parameter space in which the oscillator is energetically stable. The results are shown to be completely determined by the coefficients of the first and second cumulants of the fluctuations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
U. Frisch, inProbabilistic Methods in Applied Mathematics, A. T. Bharucha-Reid, ed. (Academic Press, New York, 1968), Vol. 1, p. 75.
R. Kubo, inStochastic Processes in Chemical Physics, K. E. Shuler, ed. (Wiley, New York, 1969), p. 101.
R. C. Bourret, U. Frisch, and A. Pouquet,Physica 65:303 (1973).
N. G. van Kampen,Phys. Rep. 24:171 (1976).
R. F. Fox,Phys. Rep. 48:179 (1978).
B. J. West, K. Lindenberg, and V. Seshadri,Physica, to be published.
V. I. Klyatskin and V. I. Tatarskii,Sov. Phys. Usp. 16:494 (1974).
R. Dashen,J. Math. Phys. 20:894 (1979).
O. M. Phillips,J. Fluid Mech. 2:417 (1957).
M. C. Wang and G. E. Uhlenbeck,Rev. Mod. Phys. 17:323 (1945).
K. Lindenberg, V. Seshadri, and B. J. West,Phys. Rev. A, to be published.
Author information
Authors and Affiliations
Additional information
Supported in part by the Office of Naval Research, NSF Grant # CHE 78-21460, and by a grant from Charles and Renée Taubman.
Rights and permissions
About this article
Cite this article
Lindenberg, K., Seshadri, V., Shuler, K.E. et al. Equal-time second-order moments of a harmonic oscillator with stochastic frequency and driving force. J Stat Phys 23, 755–765 (1980). https://doi.org/10.1007/BF01008517
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01008517