Behaviour of impact oscillator with soft and preloaded stop

New phenomena of the dynamics of oscillators with impacts, when the stiffness of the stop changes from zero to infinity, are described. Dynamics of one example of the system with soft impacts, as the model of the piercing machine, is explained in more detail by bifurcation diagrams, time series, phase trajectories and Poincarè maps of periodic and chaotic impact motions. Optimal combinations of system parameters are found for the obtaining of maximum before-impact velocities.