Many practical engineering systems include impacts and vibrations. Researchers have tried to explain the effects of these impacts by studying oscillators with a single degree of freedom. The onset of impacts corresponds to a grazing bifurcation. Studies have found good agreements between the Poincare maps and the physical measurements of these simple impacting systems. Truncating the map to the Nordmark map with a square-root singularity will approximate the dynamics near the grazing bifurcation. However, this is only useful in an extremely small parameter range. The main goal of this talk is to realize whether the reason for this is the presence of small damping. When the damping is small, the frequency of the external periodic forcing will coincide with the natural frequency of the system, giving rise to resonance. I will also talk about finding and computing curves of period-doubling and saddle-node bifurcations that will help explain the dynamics of the system.