Abstract
Statistical estimates of thermal noise fluctuation of a linear harmonic oscillator used to detect weak forces are reexamined with special reference to gravitational experiments. Thermal noise limitation on the measurement of displacement of an oscillator is studied. It is found that the signal response of an oscillator reaches the maximum value while the thermal noise response reaches the minimum value at the same time during the transient state of the oscillator, and the precision of the experiments in the transient state could increase about two orders higher than that in the equilibrium state for typical experiments. It is also found that there is an optimum duration of measurement in which the uncertainty due to thermal noise in this period is the least.
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