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

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

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Theory of Machine
For an isochronous Hartnell governor (where r₁ and r₂ = Maximum and minimum radius of rotation of balls respectively, S₁ and S₂ = Maximum and minimum force exerted on the sleeve respectively, and M = Mass on the sleeve)

S₁/S₂ = r₁/r₂
(m.g - S₁)/(m.g - S₂) = r₂/r₁
(m.g + S₁)/(m.g + S₂) = r₁/r₂
S₂/S₁ = r₁/r₂

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Theory of Machine
In a cam drive with uniform velocity follower, the sharp corners of the displacement diagram are rounded off at the beginning and at the end of each stroke. This is done

Because of difficulty in manufacturing cam profile
Because the uniform velocity motion is a partial parabolic motion
In order to have acceleration in beginning and retardation at the end of stroke within the finite limits
Because of loose contact of follower with cam surface

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