Theoretical Study of Fano Resonance in a Mechanical System

Resonance conditions are a major area of study in theoretical and experimental investigation. Normally, a resonance condition is characterized by a symmetric shape on either side of the resonance. In some cases, we can observe an asymmetric resonance shape, which is called a Fano resonance. We will study the appearance of Fano resonance in a purely mechanical system. The frequency response of the primary system is approximated using the method of multiple scales focusing on the location of the resonance condition. Then, curve fitting is used to approximate the Fano parameter associated with the system, which provides a measurement of the asymmetry in the resonance line-shape. Using this, we investigate how the various parameters associated with the system influence the strength of the Fano resonance