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

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Theory of Machine
Two heavy rotating masses are connected by shafts of lengths l₁, l₂ and l₃ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

l = l₁ + l₂.(d₁/d₂)⁴ + l₃.(d₁/d₃)⁴
l = l₁ + l₂.(d₁/d₂)³ + l₂.(d₁/d₃)³
(l₁ + l₂ + l₃)/3
l₁ + l₂ + l₃

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