Theory of Machine
A body is said to be under forced vibrations, when

A body vibrates under the influence of external force
None of these
No external force acts on a body, after giving it an initial displacement
There is a reduction in amplitude after every cycle of vibration

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform pressure, is (where r₁ and r₂ = External and internal radii of collar respectively)

(2/3). μ W (r₁ + r₂)
(1/2). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2). μ W (r₁ + r₂)
(2/3). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]

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

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