Theory of Machine
The ratio of the maximum displacement of the forced vibration to the deflection due to the static force, is known as

Magnification factor
Damping factor
Logarithmic decrement
Damping coefficient

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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)

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

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