The transient vibration problem of SDOF-system with constant natural frequency during run-up and shut-down for a linearly changing speed has already been solved by a number of authors using exact methods. However, during the transition process the natural frequency in many practical cases changes with time. In the present paper, the influence of natural frequency changes with respect to time is investigated using numerical simulation. Further, considering the computation time required, the paper suggests approximate formulas to estimate the maximum resonance amplitude during this transition. To illustrate the accuracy of the formulas, numerical results are shown in graphical formats.