By way of illustrating how group representations can be gainfully utilized in the study of oscillations of dynamical/mechanical systems with known symmetries, we study the oscillations of a simple dynamical system consisting of three identical masses with a triangular symmetry. The particles are connected by light strings having the same stiffness constant. By use of irreducible representations of the symmetry group of the dynamical system, one obtains the frequencies of the normal modes of oscillation of the system without having to solve the characteristic equation of degree six in the eigenvalue of they system. This approach greatly simplifies the determination of the motion of the system and can easily be extended to other dynamical/mechanical problems with known symmetries. (author). 9 refs, 3 figs, 5 tabs.