On the Accuracy Problem for Pendulum Clock on a Vibrating Base

Resumo

The problem of the influence of periodic vibrations of the suspension point of a physical pendulum on its nonlinear oscillations in the vicinity of a stable vertical equilibrium position is investigated. The vibrations are assumed to be periodic and occur in the plane of the pendulum motion. The approximate, time-independent equations of motion are obtained. For the case of pendulum oscillations in the vicinity of the vertical equilibrium position that is allowed by approximate equations, the action — angle variables have been introduced and it has been shown that most of the trajectories of the approximate system are also preserved in the complete system. In the plane of two dimensionless parameters: the oscillation amplitudes of the pendulum and the parameter characterizing the difference in vibration intensity values of the suspension point in the horizontal and vertical directions there are areas in which the pendulum clock is fast and areas in which it is slow.