Vibrational Normal Modes of an Equilateral Triangular Mechanical Molecule

Abstract

Three point-like massive particles/atoms are connected with three springs forming an equilateral triangle replicating a prototype triatomic molecule. The triangle is inscribed within a stationary frame via three additional springs confining the vibrations of the molecule to a 2D space. It is the objective of this research flavored investigation to seek the normal vibrational modes for this three-body six-spring structure. The entire analysis including symbolic, numeric, and graphics is carried out by adapting a suitable Computer Algebra System (CAS), Mathematica . For a comprehensive understanding, the frequency of the normal mode is used for a visual animation; an actual mechanical replica of the “molecule” for the scenario on hand is fabricated.