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 Δt/(1/λ) where Δt 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 Δt gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio Δt/(1/λ) is less than 1, the uncertainty remains substantially unchanged.