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

Resultant couple is equal to zero
Resultant force is equal to zero
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

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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)

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

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