Theory of Machine
A shaft has two heavy rotors mounted on it. The transverse natural frequencies, considering each of the rotor separately, are 100 Hz and 200 Hz respectively. The lowest critical speed is

12,000 r.p.m.
9,360 r.p.m.
5,367 r.p.m.
6,000 r.p.m.

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Theory of Machine
The maximum fluctuation of energy is the

Ratio of the mean resisting torque to the work-done per cycle
Variations of energy above and below the mean resisting torque line
Sum of the maximum and minimum energies
Difference between the maximum and minimum energies

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

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Theory of Machine
The contact ratio is given by

(Length of the arc of approach)/cosφ
(Length of the path of approach)/(Circular pitch)
(Length of the arc of contact)/(Circular pitch)
(Length of path of recess)/(Circular pitch)

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