Revisiting normal modes of coupled oscillations with Spectral Graph Theory

The 2007 classic book by David Morin entitled “Introduction to Classical Mechanics”, well known among students of Physics Olympiads, contains many exercises of coupled oscillations that inspired problems in recent exams. In this paper, we present these problems, including their solutions and computational simulations using advanced features of Desmos, a free online graphics system. Moreover, we show a more didactic general way of handling such problems, even the most complex ones, using Linear Algebra and Graph Theory.

Keywords:
Mechanics; Coupled oscillations; Eigenvalues; Eigenvectors; Computational physics; Graph Theory