In the measurement of G with the angular acceleration method,the improved correlation method developed by Wu et al.（Wu W H,Tian Y,Luo J,Shao C G,Xu J H and Wang DH 2016 Rev.Sci.Instrum.87 094501） is used to accurately estimate the amplitudes of the prominent harmonic components of the gravitational background signal with time-varying frequency.Except the quadratic slow drift,the angular frequency of the gravitational background signal also includes a cosine oscillation coming from the useful angular acceleration signal,which leads to a deviation from the estimated amplitude.We calculate the correction of the cosine oscillation to the amplitude estimation.The result shows that the corrections of the cosine oscillation to the amplitudes of the fundamental frequency and second harmonic components obtained by the improved correlation method are within respective errors.
Using the relativistic Lagrangian expression,we develop a method to derive the equation of motion of the torsion balance in a non-inertial reference frame,which is used to analyze the gravitational experiment in measuring Newton's constant G with the angular acceleration method.Our calculation shows that the Earth's rotation couples with the vibration,which should be considered in the high-accuracy experiments of determining the gravitational constant G.
