Linear Electrostatic Oscillator With Viscous Damping

Abstract

Abstract Experimental analysis of a translating spring-mass system with a constant electrostatic force in the presence of viscous damping is presented. The challenge in this effort has been to develop an analytical model for the electrostatic system and experimentally extract numerical values for viscous damping and the very small electrostatic force. The system has dynamical equations of motion similar to that of a homogeneous spring-mass system with no external force in the presence of viscous damping. The electrostatic parallel plate system includes the addition of a conservative electrostatic potential energy term corresponding to an electrostatic restoring force. The electrostatic force is conservative and opposes the direction of motion when the position of the oscillating mass being acted upon is greater than or less than zero. Another, similar system comparison can be made between the electrostatic one and that of a translating system acted upon by friction alone. However, the frictional force, unlike the electrostatic one presented here, is non-conservative and, also unlike the electrostatic force, opposes the direction of velocity when the oscillating mass being acted upon is greater than or less than zero. From empirical data, parameters of the translating electrostatic system are determined and cross-verified by more than one method. A state-space model is developed using the Lagranian formalism which includes a dissipative viscous damping term. Results are simulated in Matlab numerically. These simulated results are compared to measured data. Applications of the electrostatic force in a translating set-up are discussed and concluded.