Typically, small oscillations about a stable equilibrium point are simple harmonic motions with frequency determined by the second derivative of the potential energy evaluated at the equilibrium point. There are anomalous cases, however, in which the second derivative vanishes and the fourth order term dominates the expansion of the potential energy in the neighborhood of the minimum. In this case, the small oscillations are described by the quartic oscillator. By means of a simple example, in which the said anomaly occurs, the quartic oscillator is discussed and it is shown how its equation of motion can be solved in terms of Jacobi elliptic functions. The example affords the opportunity to familiarize undergraduate students with these important functions that do not appear in the standard physics curriculum.
Keywords:
small oscillations; quartic oscillator; Jacobi elliptic functions
