Small vibrations of a mechanical system consisting of three particles connected by springs and placed in each vertex of the equilateral triangle is appropiate for illustrating the gauge symmetry breaking and the vacuum stability conditions of a minimal $S_3$-invariant extended Higgs potential. In the $S(3)$ extended Standard Model, there are three $SU(2)$ Higgs doublets that belong to a singlet $H_S$ and a doublet representation $H_1$, $H_2$ of the $S_3$- flavour group, which is isomorphic to the equilateral triangle symmetry group.
It is possible to describe the$S(3)$ Higgs model in terms of nine invariants $x_i$, the configuration or state of a clasical mechanical vibrating triangle consisting of three masses connected by springs and placed in each vertex of the equilateral triangle may be conveniently descibed by a 9-dimensional vector $\bf X$ where 9 is the number of degrees of freedom. In the present article we explore the parallels between the clasical mechanical system and the Three $S(3)$ Higgs Potential. The parallel is completed adding effective $O(2)$ operators to the $S(3)$ SM lagrangian, the extra terms analog to the classical kinetic energy $T$ play the role of Weakly Interacting Massive Particles.