This study investigates the transient and steady state solutions of a single-degree-of-freedom (SDOF) piecewise-linear system subjected to double excitations with the frequencies of rational ratio. Based on theoretical analysis and numerical simulation of the 4th order Runge-Kutta method, both waveform and phase portrait are plotted in good agreement with periodic motions of the piecewise-linear system in different steady state parameters when periodic motion and chaotic motion are distinguished by bifurcation diagrams with characteristics of phrase portraits, frequency spectrum, Poincaré sections and Lyapunov exponent.