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However, in a practical view point, these diagnosis systems have the following defects: (1)The probability that a resonance due to a crack occurs in the rated speed range is small. (2)It is very dangerous to observe vibration characteristics in resonance ranges spending long time. In this paper, we propose a new method utilizing the changes of vibration phenomena due to a crack in a nonstationary oscillation during start up of a rotating machinery. The advantage of this method is that we can check the signals denoting the occurrence of a crack in a wide speed range by a single sweep and also can avoid the operation in dangerous resonance ranges. 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