On the Distribution of Energy between the Vibration Modes

Abstract

The initial energy of a conservative mechanical system is distributed between its vibratory modes. It is a known fact that if the system is displaced according to a certain mode shape and released with zero velocity then it vibrates only in that mode. In this study it is investigated whether it is possible, through appropriate selection of initial conditions, for energies in different modes to take prescribed ratios of the total energy. Keeping in mind the difficulties of many students with regard to modal quantities, a systematic treatment of the energy distribution between the modes is given. In doing so, the known results in the literature are pointed out as special cases. At the end of the paper two examples are given.