Hard vs soft impacts in oscillatory systems' modeling revisited.

An application of soft and hard impact models to represent vibro-impact systems is reconsidered. The conditions that the two collision models have to satisfy to be equivalent in terms of energy dissipation are discussed and key features of the resulting soft impact models are demonstrated. Then, it is examined what effect will be exerted on the behavior of a vibro-impact system when an additional elastic-damping element and external forcing are used.