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)

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

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Theory of Machine
A rotor which is balanced statically but not dynamically is supported on two bearings L apart and at high speed of the rotor, reaction on the left bearing is R. The right side of the bearing is shifted to a new position 2L apart from the left bearing. At the same rotor speed, dynamic reaction on the left bearing in the new arrangement will

Become equal to R/4
Become equal to R/2
Become equal to 2R
Remain same as before

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