Past exam of the mathematical methods II course of the University of Oxford 2016 9 b Solution 2026-10-25
A normal mode has a fixed pattern of relative displacements, with every coordinate proportional to one common time-dependent factor. There are three independent normal modes in this three-coordinate model: two internal vibrations and one zero-frequency rigid-body translation. The latter moves all three atoms together without stretching either spring. This count concerns the specified one-dimensional model, rather than a molecule with unrestricted three-dimensional motion.