Theory of Machine
A body is said to be under forced vibrations, when

A body vibrates under the influence of external force
There is a reduction in amplitude after every cycle of vibration
None of these
No external force acts on a body, after giving it an initial displacement

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Theory of Machine
A system of masses rotating in different parallel planes is in dynamic balance if the

Resultant force is numerically equal to the resultant couple, but neither of them need necessarily be zero
Resultant force and resultant couple are both equal to zero
Resultant force is equal to zero
Resultant couple is equal to zero

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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 cosθ
m.ω².r (cos 2θ/n)
m.ω².r sinθ

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