Resonance in impact problems

This article is motivated by an engineering problem: given a mechanical system with some amount of looseness, is it possible to identify this looseness using only dynamical testing? Such a possibility would permit automated testing, frequent and cheap monitoring, and would be particularly useful in hostile environments. erstand this question, we considered a model of the following mechanical setup (see Figure 1). A U-shaped mobile part is joined to a massive solid support by a linear elastic spring and a damper; the mobile part is submitted to a sinusoidal excitation. It is assumed that the motion is one dimensional.