Does the Time-of-Swing Method Give a Correct Value of the Newtonian Gravitational Constant?

Abstract

A standard way of measuring the Newtonian gravitational constant has been the time-of-swing method using a torsion pendulum. A key assumption is that the spring constant of the torsion fiber is independent of frequency. This is likely to be true to a good approximation if any damping present is proportional to velocity. However, recent work on the elasticity of flexure hinges suggests that typically the damping at low frequency is best modeled by including a frequency-independent imaginary component in the spring constant. In this case, the real part of the spring constant must vary, leading to an upward bias in a measurement of $G$.