Influence of the colored noise on determining the period of a torsion pendulum

Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio Δ t /(1/ λ ) where Δ t is the interval of the sample time and 1/ λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time Δ t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio Δ t /(1/ λ ) is less than 1, the uncertainty remains substantially unchanged. (paper)