Theory of Machine
Sensitiveness of the governor is defined as the ratio of the

Mean speed to the minimum equilibrium speed
Difference of the maximum and minimum equilibrium speeds to the mean speed
Mean speed to the maximum equilibrium speed
Sum of the maximum and minimum equilibrium speeds to the mean speed

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Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ωr [cos θ + (cos 2θ/n)]
ω²r [sin θ + (sin 2θ/n)]
ω²r [cos θ + (cos 2θ/n)]
ωr [sin θ + (sin 2θ/n)]

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Theory of Machine
In a mechanism, the fixed instantaneous centers are those centers which

Vary with the configuration of the mechanism
Remain in the same place for all configurations of the mechanism
Moves as the mechanism moves, but joints are of permanent nature
None of the listed here

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Theory of Machine
The primary 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 cosθ
m.ω².r sinθ
m.ω².r (sin 2θ/n)
m.ω².r (cos 2θ/n)

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