An Electrostatic Oscillator Experiment

Martin, D. H.; Longbrake, R. L.

doi:10.1119/1.1986559

Cited by 5 publications

(4 citation statements)

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“…The electrostatic pendulum is a well-known and commonly used experiment; it is appropriate for demonstrating the influence of electrostatic force on charged objects and can be used at different levels of education, from secondary to tertiary education. In the literature, this experiment was qualitatively well explained [1][2][3] and there also exist some quantitative analyses [4,5].…”

Section: Introductionsupporting

confidence: 54%

“…The capacitor plate was considered as an equipotential surface and by using a relaxation method, first the charge on the ball was calculated and then the frequency. The results of the model were compared with the experimental data obtained by Martin and Longbrake [4] and larger deviations were observed only for larger distances between the capacitor plates. As the main reason for these deviations, Asano [5] claimed that the coefficient of restitution would need to be measured more accurately.…”

Section: Introductionmentioning

confidence: 95%

“…Martin and Longbrake [4] studied the electrostatic pendulum experimentally and also proposed a simple mathematical model. They found that the frequency of the pendulum linearly depends on the voltage between the capacitor plates.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modelling of the electrostatic pendulum in school and undergraduate education

2013

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The electrostatic pendulum, also known as the electrostatic ping-pong, is an exciting experiment in school as well as in undergraduate education. We can easily demonstrate how the frequency of the electrostatic pendulum depends on the voltage across the capacitor. In this paper, we develop a simple mathematical model describing the dynamics of this experiment. In a step-wise manner, we introduce the external forces influencing the dynamics of the electrostatic pendulum. First, we take into account the electric force only. Then, we add air resistance and the non-elasticity of ball collisions with the capacitor plates. The model predictions show that the non-elastic collisions have greater effect on the pendulum dynamics than air resistance; in particular, this is true for higher frequencies of the pendulum. For lower frequencies, however, gravity is of crucial importance. The mathematical model is implemented in a graphic-oriented computer program, which gives the possibility of using this theoretical analysis also at the secondary school level.

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Section: Introductionsupporting

confidence: 54%

Section: Introductionmentioning

confidence: 95%

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Mathematical modelling of the electrostatic pendulum in school and undergraduate education

2013

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“…Various types of modeling approaches have been proposed for self-excited electrostatic actuators [21,23,25,26]. This study employed a method based on the capacitance between the plates of the armature and electrodes, which were used in previous studies using plate-shaped armatures [21,23].…”

Section: Effect Of the Elastic Element On The Electrostatic Self-excimentioning

confidence: 99%

Effect of elastic element on self-excited electrostatic actuator

Nabae

Ikeda

2018

Sensors and Actuators A: Physical

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Self-excited electrostatic actuators, which are also called Franklin bells or Gordon bells, are one of the simplest oscillators among various types of actuators. The actuators oscillate with DC voltage and simple structures mainly composed of only two electrodes and a conductive armature. These features seem suitable for micro mechatronic devices, including micro robots; however, these actuators only have small number of practical applications. The high voltage for actuation, damage by electrical discharge, and mechanical loss with collisions between the armature and electrodes keep the actuators away from practical usages. This research focuses on the mechanical loss with collisions between the armature and electrodes and proposes a method for decreasing this loss by energy recovery with elastic elements. This study first conducts a model-based analysis of the behavior of the proposed system that combines the electrostatic self-excitation and the elastic elements. The results are then compared with the experimental results of a prototype actuator. The simple analysis predicted the increase of the oscillating frequency with the elastic elements, limiting the condition of the self-excitation caused by the energy loss of the damping factor. The results of the experimental verification showed the same tendency as the analytical predictions: increase of the oscillating frequency and existence of a critical value for the oscillation limit. Although comparatively large errors were confirmed between the simulation and the experiment under a lower applied voltage, experimentally obtained frequencies have errors less than 6.4% compared with the analytical result under the applied voltage of over 1.3 kV.

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