Collision dynamics of two adjacent oscillators

A linear analysis is made of a single collision between two single-degree-of-freedom systems separated by a gap. The contact is modelled by a spring and a viscous damper. The approach is to describe the motion of the pair as being composed of sum and difference displacements. The equation of motion during contact is found and the solution is obtained from the conditions at initial contact. The main parameters are the ratio of strain energy to kinetic energy at initial contact, and the damping of the contact. The contact time and the energy loss are calculated, which gives an expression for the coefficient of restitution for the collision. This coefficient is found to be dependent on the collision velocity, but becomes constant for strong collisions.