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 Delta t/(1/lambda) where Delta t is the interval of the sample time and 1/lambda is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time Delta t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio Delta t/(1/lambda) is less than 1, the uncertainty remains substantially unchanged.