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
When a mass of a critically damped single degree of freedom system is deflected from its equilibrium position and released, then it will

Oscillate with decreasing amplitude
Return to equilibrium position without oscillation
Oscillate with increasing time period
Oscillate with constant amplitude

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