> Does anyone know of an example of a simple physical system where eigenvalues have a physical interpretation? Oscillation modes in mass-spring systems. Here i

> Does anyone know of an example of a simple physical system where eigenvalues have a physical interpretation? Oscillation modes in mass-spring systems. Here is a simple one with 2 masses and 3 springs, so the matrix is only 2-by-2. https://math24.net/mass-spring-system.html https://math24.net/mass-spring-system.html With more than 2 masses, you don't need to arrange the masses on a line, but you can have a 2d or 3d arrangement, with interconnecting springs. I am sorry I failed to find an example image. The theory is explained, for example, around page 479 in this Thornton and Marion Classical Dynamics textbook. But you need to read about Lagrangian mechanics (chapter 7) before it makes sense. https://eacpe.org/app/wp-content/uploads/2016/11/Classical-Dynamics-of-Particles-and-Systems.pdf https://eacpe.org/app/wp-content/uploads/2016/11/Classical-D...