A dynamic system having multiple degrees of freedom and being under parametric excitation has been studied in an earlier paper [2]. However, the analysis given there necessitates certain restrictions on the distribution of the natural frequencies of the system. In this paper those restrictions are removed. The analysis presented here shows how to obtain a constant matrix whose eigenvalues determine the stability or instability of a system of ordinary differential equations with periodic coefficients at a given excitation frequency. The constant matrix is expressed entirely in terms of the given system parameters and the excitation frequency.