Theory of Machine
In under damped vibrating system, the amplitude of vibration

Decreases linearly with time
Increases exponentially with time
Increases linearly with time
Decreases exponentially with time

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

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

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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)

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

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