On the zero shift problem of a vertical pendulum

The effect of the vibration transmitted through pendulum support on the accuracy of a pendulum used as a vertical reference is examined. Based upon the method of equivalent linearization of Kryloff and Bogoliuboff together with a perturbation scheme, the average angular displacement of a vertical pendulum is obtained in terms of the functional averages involving support excitations. It is shown that the method leads to general and simple formulas for estimating the zero shift and, in the case of random support excitations, second-moment properties. The analysis is valid for both heavily damped and weakly damped systems. The zero shifts due to several types of deterministic and random excitations are computed. Methods of minimizing the zero shift are considered for these cases.