Theory of Machine
The equation of motion for a vibrating system with viscous damping is (d²x/dt²) + (c/m).(dx/dt) + (s/m).x = 0, if the roots of the equation are __________ then the system will be under damped.

Complex conjugate
None of these
Equal
Real

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

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