RESONANCE REPULSION IN A COUPLED TORSIONAL OSCILLATOR

Abstract

A mechanical system is developed and investigated to demonstrate properties of two coupled oscillators. The experimental setup consists of masses clamped to a single steel wire used as a torsion oscillator and optical lever to monitor the motion of the system. Adjustment of the spacing between the masses allows for the coupling strength between the two oscillators to be varied. The primary feature of the system examined in this work is the shifting of the resonant frequencies of the coupled oscillators from the resonant frequencies of the isolated oscillators, an effect known as resonance repulsion. The isolated oscillators are underdamped. The coupling strength between the two oscillators is varied by changing the length of wire between the two. The length was varied by a factor of ten. Damping rates and resonant frequencies of the isolated oscillators are measured in order to model the coupled oscillator system. Theoretical predictions for the magnitude of the resonance repulsion effect are compared to experimentally determined values. For the weakest coupling conditions, where small measurement uncertainties may have a large impact, the disagreement between theory and experimental values for resonance repulsion is only 5%. For conditions of strongest oscillator coupling, the two resonances were observed to separate by a factor of 14.07 when compared to the resonant frequency separation in the uncoupled oscillator. For the strongest coupling case the experimental angular frequency separation is 39.22/s, theoretical is 39.40/s, and the uncoupled separation in the original isolated oscillators is 2.80/s.