Abstract
Summary According to the Hertz theory, impact between an elastic surface and an elastic sphere is characterized by a non-linear restoring force. In this paper, another mass is connected to the sphere by means of a massless, linear spring. One dimensional impact of this mass-spring-mass system is analyzed. Energy considerations lead to maximum attainable values of the impact force and rebound velocity. Digital solutions of the governing non-linear differential equations are used to obtain typical force-time histories during impact. The digital results are summarized in a non-dimensional form suitable for predicting maximum impact force, duration of contact and rebound velocity for a wide range of initial conditions and system parameters.
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