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

The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. Generally, the stationary environmental noise is modeled as a white noise, and contributes to the period uncertainty as a function of the initial amplitude, the quality factor, the variance of noise and the time length. As to a sudden sharp disturbance acting on the pendulum, a narrow impulse model is constructed. It results in a sharp jump in the phase difference, which can be excluded with the 3σ criterion for a correction. An experimental data analysis for the measurement of the gravitational constant G with the time-of-swing method shows that the period uncertainty due to the environmental noise is about one and a half times the fundamental thermal noise limit. Though this result is dependent on the ambient environment, the analysis is instructive to improve the measurement accuracy of experiments.