Models for rotating rigid discs excited by contact elements have been developed for the study of break noise and vibration. More recently, models for clutch squeal/eek noise have been developed as well. Such phenomenological representations, even though simple, are of great help for designers given that many physical features can be included, such as the circulatory and gyroscopic effects. Instability or self-excited vibrations are represented by wobbling motions. In this study, a device is included as a disc connected to the primary system by a set of spring and damping elements. A complex coordinate notation was helpful to make a concise physical description of the in-phase and out-of-phase wobbling motions between the bodies. If its properties are properly adjusted, all modes interact (indicating veering or crossings between the eigenvalue loci), and the system is stabilized.