In this note we present some numerical simulations of the asymptotic behaviour of a Harmonic Oscillator Differential Equation, within the framework of a recently defined generalized differential operator. To obtain these results, we have not proceeded as in the published results: varying the functions of the right-hand side of the system considered, but, on the contrary, in the differential operator used, the nuclei and the order used have been varied. In this way, a greater scope and generality are provided to the results obtained, which complement some known in the literature.