The response of an oscillatory system to excitation by a transient displacement

Abstract The response of a conservative linear system to a transient applied force of some prescribed form is shown, with suitable interpretation, to be the same as that due to excitation by a transient displacement of the same form. Consequently the solution of practical vibration problems involving ‘time-dependent boundary conditions’ (with their attendant mathematical complexity) is greatly simplified and given a readily understood physical significance. In the development of the theory, the concepts of ‘effective modal stiffness’ and ‘effective modal mass’ (which have occasionally been invoked in the past, and in more senses than one) are elucidated.