Forced oscillations with linear and nonlinear damping

Abstract

A general solution is derived for the differential equations of forced oscillatory motion with both linear damping (∼v) and nonlinear damping (∼v2). Experiments with forced oscillators are performed using a flat metal plate with a drag force due to eddy currents and a flat piece of stiffened cardboard with a drag force due to air resistance serving as the linear and nonlinear damping, respectively. Resonance of forced oscillations for different damping forces and quality factors is demonstrated. The experimental measurements and theoretical calculations are in good agreement, and damping constants are determined.