The study and teaching of the vibrational modes of the triatomic molecule

This work shows that by means of knowledge of the general theory of small oscillations is possible to solve analytically the vibrational modes of the triangular molecule, and from comparative results between the linear and triangular molecule can access the dynamics of the triangular molecule and simplify the analysis. To illustrate this, is modeled mechanically a triatomic molecule using the Lagrangian formulation and assuming a type of molecule in which the masses (atoms) are located at the vertices of a triangle. For an analytical treatment of the problem we use the theory of small oscillations, considering equal masses (atoms) and coupling constants. This allows to write the Lagrangian, and then to obtain dynamical equations for determining normal vibration frequencies. The case of the linear triatomic molecule is analyzed and discussed, determining the corresponding vibrational normal modes. Finally, the solutions for both cases are compared.