Abstract: An analysis is presented for determining the dynamical responses for a class of multi degree of freedom systems with clearances or gaps. The systems consist of linear components, but the maximum displacement of one of the masses is limited to a threshold value by a rigid wall. The system is uncoupled by using modal matrix approach. Based on the impacting condition and the matching condition according to the impact law, we have derived the periodic motions and their stability conditions. Then, applying th...