Observing forced oscillations using a charge generator and a homemade capacitor

Abstract In this work, we present a didactic experiment involving the observation of forced oscillations in the vertical plane induced by an electric force acting on a dielectric cylinder that forms part of a mass-spring system. The cylinder is placed on a homemade Leyden jar-type capacitor, which is charged over time by a Van de Graaff-type electrostatic generator. Simultaneously, the motion of the cylinder is recorded using a smartphone camera, and the video is later analysed with the Tracker software. During the recording, the generator is switched on for a period, then turned off, and finally, the capacitor is discharged. We developed a simplified theoretical model to describe the cylinder’s motion during the three regimes, allowing us to understand the forced oscillations and the displacement of the system’s stable equilibrium position immediately after the generator is switched on. In the regime of small oscillations, we demonstrate that the system behaves as a forced oscillator with variable frequency when the charge generator is active, due to the coupling between the system’s time-dependent charges and the cylinder’s displacement. Finally, we use the modelling, combined with video analysis, to show the possibility of obtaining an estimate of the product of the charges that remain in the system immediately after the generator is turned off, even when detecting displacements on the order of the experimental uncertainty limit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mtext>mm</mml:mtext> </mml:mrow> </mml:math> .