On the Frequency sweep test, it is very important as to how the sweep rate, which effects the response, should be chosen. If the sweep rate is too fast, the maximum response and the natural frequency can not be measured correctly. On the other hand, if the sweep rate is too late, the oscillation time is too long and the possibility of the failure in the specimen is increased. In this paper, in order to clarify the vibrational characteristics and decide the sweep rate, the equation of the oscillation on the one degree of freedom vibration system under the frequency sweep test has been solved by the Runge-Kutta-Verner fifth and sixth order method. From these results, it is shown that the relationship between the sweep rate and the response leads to dimensionless forms. Consequently the simple formulas which decide the relationship between the sweep rate and the maximum response or the resonance frequency have been obtained.