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
0.571/ √δS
0.6253/ √δS
0.5615/ √δS

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Theory of Machine
The frictional torque transmitted in a truncated conical pivot bearing, considering uniform pressure, is

(1/2). μ W cosecα [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3). μ W cosecα [(r₁³ - r₂³)/(r₁² - r₂²)]
(2/3). μ W cosecα (r₁ + r₂)
(1/2). μ W cosecα (r₁ + r₂)

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