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This work revisits a couple of well-known piecewise linear oscillators pointing
out several unnoticed properties. In particular, for one of these oscillators
we study under what conditions bounded motions are possible and investigate the
effect of viscous damping on its trajectories. The article
complements a relatively recent paper by Capecchi [10] and presents a non-trivial
counterexample to the wide-spread belief according to which chaos is ubiquitous in piecewise
linear systems.