The period of a free-swinging pendulum in adiabatic and non-adiabatic gravitational potential variations

An experiment aimed at the determination of the Newtonian constant of gravitation G is in progress at the Politecnico di Torino. This experiment is based on measurement of the period of a simple pendulum, when its gravitational potential is forced to cycle by moving two source masses between two positions, respectively, near and far from the oscillation plane. In previous papers various geometrical and physical effects were analysed, including internal, environmental and technical ones. Most effects are made irrelevant at the desired level of uncertainty (10−4) by the common mode rejection provided by the differential measurement scheme. The remaining effects were shown to impose reasonable constraints of symmetry and geometrical accuracy, and are quickly reviewed here. In this paper the energy exchange between the oscillating mass and the gravitational potential is analysed, and its effect on the period is evaluated. It is shown that the uncertainty contribution of the latter does not constitute a problem for the desired 10−4accuracy of G determination