Theory of Machine
The natural frequency of free transverse vibrations due to a point load acting over a simply supported shaft is equal to (where δ = Static deflection of a simply supported shaft due to the point load)

0.4985/√δ
0.6253/√δ
0.571/√δ
0.5615/√δ

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Theory of Machine
In a steam engine, the earlier cut-off with a simple slide valve may be obtained by increasing the steam lap and the angle of advance of the eccentric but keeping constant the travel and lead of the valve, this method will

Reduce maximum opening of port to steam
Cause withdrawing or throttling of steam
All of the listed here
Reduce length of effective stroke of piston

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