Three demonstrations of degeneracy lifting

Abstract

Two normal modes of vibration of a single object having exactly the same frequency are said to be degenerate modes. Certain simple systems, such as a circular membrane, have predictable degenerate modes. A lack of isotropy in the material or a geometric asymmetry can separate the frequencies and lift the degeneracy. Demonstration of this effect is easily accomplished in the classroom. Three methods of showing the effect are presented using a handbell, a short metal rod, and a coffee mug.