A realistic model of the general solution of the frequency of oscillations of an electrostatic pendulum

Věnováno doc. Oldřichu Lepilovi k jeho 90. narozeninám

Abstract

The electrostatic pendulum, like the Van de Graaff generator (VdGG), is an essential demonstration tool for physics teachers when explaining electrostatic phenomena. It is usually used to demonstrate the work done by the electric field of a plate capacitor in transferring a charged ball to a table tennis table. In the introduction of this paper, we briefly mention various theories of electrostatic pendulum dynamics involving either the influence of the electric field only or also gravitational forces or other influences. In this paper, we first compare the different models with each other with real experimental results of oscillation frequency measurements and then propose a realistic model of the physical pendulum oscillation, which provides a general solution including both the electric and gravitational forces acting on the pendulum and the restitution coefficient. In the second part of the paper, we attempt to explain the value of the coefficient, which represents the fraction of charge transferred when the pendulum contacts the capacitor plate, by comparing the discharge time constant of the VdGG with a surrogate RC circuit. In explaining the theory describing the motion of a real physical pendulum, we simultaneously differentiate the relationships for the frequency of the pendulum at each level from high school to college course. We will also show how the results of this work can be applied in high school laboratory exercises to measure VdGG as a high-voltage source in an electrostatic pendulum experiment. The conclusions, however, apply in general to any high-voltage source used.