Theory of Machine
The rotating shafts tend to vibrate violently at whirling speeds because

The system is unbalanced
Resonance is caused due to the heavy mass of the rotor
Bearing centre line coincides with the axis
The shafts are rotating at very high speeds

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Theory of Machine
The secondary 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 cosθ
m.ω².r sinθ
m.ω².r (cos 2θ/n)

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Theory of Machine
In order to give a complete secondary balance of a multi-cylinder inline engine,

None of these
Both (A) and (B)
The algebraic sum of the secondary forces must be equal to zero
The algebraic sum of the couples about any point in the plane of the secondary forces must be equal to zero

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