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Whirling of shafts

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A shaft is supported in bearings which do not impose any flexural constraint. The bearings are 1.6m
apart and the shaft carries two equal pulleys between the bearings, each 0.4m from the nearest bearing.
When the shaft is at rest the central deflection is observed to be 0.8mm. Determine the lowest whirling
speed of the shaft. Answer 20.75 rev/s; 20.4rev/s assuming parabolic curve
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