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No shaft can ever be perfectly straight or perfectly balanced. When an element of mass is a distance ' ' from the axis of rotation, centrifugal force, will tend to pull the mass outward. The elastic properties of the shaft will act to restore the "straightness". If the frequency of rotation is equal to one of the resonant frequencies of the shaft, whirling will occur. In order to save the machine from failure, operation at such whirling speeds must be avoided. Whirling is a complex phenomenon that can include harmonics but we are only going to consider synchronous whirl, where the frequency of whirling is the same as the rotational speed.

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