The effect of damping on rigid block motion under harmonic forcing

The effect of damping on the response of a rigid block to harmonic excitation is considered. It is shown that the structure seen in the absence of damping is preserved in this case. Multiple solutions, asymmetric responses, period- and impact-doubling cascades still occur, albeit in different parts of parameter space. Explicit expressions are given for the stability boundaries. It is shown that, at certain values of the forcing frequency, the stability boundaries possess a local maximum as a function of the damping.