Dynamics and stability of a two degree of freedom oscillator with an elastic stop

A two degree of freedom oscillator with a colliding component is considered. The dint of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes to a finite value to an infinite one. Several cases are. considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are,found in analytical form. In the case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic: motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases.