Recently, the minimal expressions governing the periodic solutions of any autonomous undamped piecewise-linear system with one single purely elastic impact have been derived for any number of degrees of freedom and number of impacts per period (ipp). In the present work, these results are used to exhibit the spectrum of an elementary two-degree-of-freedom vibro-impact oscillator for one, two, and three ipp. The relation between various branches in the Frequency–Energy diagram are discussed. Periodic motions with increasing ipp are shown to converge towards periodic motions with non-zero contact duration. Stability is left for future work.