Theory of Machine
The velocity of piston in a reciprocating steam engine is given by (where ω = Angular velocity of crank, r = Radius of crank pin circle, θ = Angle turned by crank from inner dead center, and n = Ratio of length of connecting rod to the radius of crank)

ωr [cos θ + (cos 2θ/n)]
ω²r [cos θ + (cos 2θ/n)]
ωr [sin θ + (sin 2θ/n)]
ω²r [sin θ + (sin 2θ/n)]

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

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

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Theory of Machine
In gears, interference takes place when

The tip of a tooth of a mating gear digs into the portion between base and root circles
Gears do not move smoothly in the absence of lubrication
Gear teeth are undercut
Pitch of the gears is not same

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