We consider the dynamic response of a single-degree-of-freedom system subjected to nonharmonic excitation. The model consists of a mass attached to a linear spring and a linear viscous dashpot impacting a rigid obstruction witha coefficient of velocity restitution. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out by using the piecewise linear feature. Period-doubling bifurcations, tangent bifurcation, and crisis occur in our model. Some parameter regions which contain no simple stable periodic motions are shown to possess chaotic motions. Lyapunov exponents are computed over a range of forcing periods. Discrete mapping is used to calculate the Lyapunov exponents for the piecewise linear system due to the fact that the discontinuity occurs at impact with the Stop.