Theory of Machine
A shaft has two heavy rotors mounted on it. The transverse natural frequencies, considering each of the rotor separately, are 100 Hz and 200 Hz respectively. The lowest critical speed is

6,000 r.p.m.
12,000 r.p.m.
9,360 r.p.m.
5,367 r.p.m.

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

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