Mathematics – Probability
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt........16g&link_type=abstract
Thesis (PH.D.)--SYRACUSE UNIVERSITY, 1995.Source: Dissertation Abstracts International, Volume: 56-09, Section: B, page: 4933.
Mathematics
Probability
2
Scientific paper
Brownian motion is a well known limit to precision experiments, and it is also going to be a limiting factor in the sensitivity of interferometric gravitational wave detectors. The power spectral density of Brownian motion depends dramatically on the strength and frequency dependence of the energy dissipation in the system of interest. We present here the measurement of Brownian motion of a simple oscillator, a torsion pendulum, where the energy losses are due to internal friction in the suspension fiber. We calculate from these measurements the power spectrum S _theta(f) of the Brownian motion, as well as other statistical functions defined in irreversible thermodynamics, such as the autocorrelation function and conditional probability distributions. We also present a measurement of internal friction as a function of frequency. With this and the physical parameters describing the pendulum, we use the fluctuation -dissipation theorem to calculate S_theta(f). . We then compare the prediction and measurement of S_theta(f), and show excellent agreement over a decade in frequency around the pendulum frequency. The spectrum S_theta(f) is not flat below resonance, and in fact follows a S_theta(f)~1/f law.
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