Abstract A study on the torsional vibrations of the drive shafts of mechanisms having variable inertia has been presented in a previous paper by the authors. The drive shaft has been assumed to be a continuous element with distributed mass. Continuous element modelling of the shaft leads to a different mathematical formulation. In this previous paper, the boundary value problem of torsional vibrations of a drive shaft has been formulated and the forced response has been examined. In the analysis, a simpler form of boundary condition for the motor side of the shaft has been considered. In this paper, the analysis is extended to a more general boundary condition of the motor side of the shaft. For this purpose, two solution techniques, a series solution method and a perturbation solution, are given and the effects of motor characteristics on the behavior of the drive shaft are examined.