Theory of Machine
A system of masses rotating in different parallel planes is in dynamic balance if the

Resultant force and resultant couple are both equal to zero
Resultant force is numerically equal to the resultant couple, but neither of them need necessarily be zero
Resultant couple is equal to zero
Resultant force is equal to zero

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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)

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

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