The unexpectedly small coefficient of restitution of a two-degree-of-freedom mass-spring system and its implications

When two elastic solids collide with each other, the coefficient of restitution (COR) is generally considered to be unity based on the notion that the elastic strain energy will be fully released and the kinetic energy and momentum are conserved. This statement, with the support of numerous experiments of ball collision, is so widely acknowledged that people rarely realize that the COR of pure elastic collision can be significantly smaller than unity under some circumstances. The missing part in the story is the vibrational energy stored in the reciprocal motion of materials or structural components relative to the centre of mass. This article is to unveil the striking effect of elastic vibration using the most concise mass-spring system and demonstrate that the COR can even be as small as 0.178. We then discuss the effects of plasticity, non-linear elasticity and increased number of degrees of freedom and conclude the implication of small COR in crashworthiness design.