On lightly damped linear systems

A simple engineering approximation using undamped modes is shown to be valid for determining the effect of small viscous or equivalent viscous-type damping forces on the forced vibration response of a lightly damped linear systems. It is shown that intermodal coupling of the undamped modes may be neglected with negligible error, except when the system has degenerate or quasi-degenerate modes. This can occur in complex structural systems such as aircraft or spacecraft. In such cases, one of these two modes has virtually no damping, whereas the other effectively has the damping of both.