Exceptional points in two simple textbook examples

Abstract

We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant coefficients. The second one is the well known damped harmonic oscillator. They enable one to connect the occurrence of linearly dependent exponential solutions with a defective matrix that cannot be diagonalized but can be transformed into a Jordan canonical form.