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

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Theory of Machine
A rigid body, under the action of external forces, can be replaced by two masses placed at a fixed distance apart. The two masses form an equivalent dynamical system, if

The sum of the two masses is equal to the total mass of body
The sum of mass moment of inertia of the masses about their center of gravity is equal to the mass moment of inertia of the body
All of these
The center of gravity of the two masses coincides with that of the body

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