Theory of Machine
In a Hartnell governor, the lift of the sleeve is given by (where r₁ and r₂ = Max. and min. radii of rotation, x = Length of ball arm of the lever, and y = Length of sleeve arm of the lever)

(r₁ - r₂) (y/x)
(r₁ - r₂) (x/y)
(r₁ + r₂) (y/x)
(r₁ + r₂) (x/y)

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Theory of Machine
A body is said to be under forced vibrations, when

None of these
A body vibrates under the influence of external force
There is a reduction in amplitude after every cycle of vibration
No external force acts on a body, after giving it an initial displacement

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Theory of Machine
The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r (cos 2θ/n)
m.ω².r cosθ
m.ω².r sinθ
m.ω².r (sin 2θ/n)

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