Theory of Machine
The natural frequency of free transverse vibrations due to uniformly distributed load acting over a simply supported shaft is (where δS = Static deflection of simply supported shaft due to uniformly distributed load)

0.4985/ √δS
0.6253/ √δS
0.571/ √δS
0.5615/ √δS

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Theory of Machine
The static balancing is satisfactory for low speed rotors but with increasing speeds, dynamic balancing becomes necessary. This is because, the

Unbalanced couples are caused only at higher speeds
Effects of unbalances are proportional to the square of the speed
Unbalanced forces are not dangerous at higher speeds
Effects of unbalances are directly proportional to the speed

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