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In this lecture I will discuss linear oscillators undergoing impact with secondary elastic supports, which are studied experimentally and semi-analytically for near-grazing conditions [1].We discovered a narrow band of chaos close to the grazing condition and this phenomenon was observed experimentally for a range of system parameters.Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits,created at "invisible" grazing, take part.