Theory of Machine
In under damped vibrating system, if x₁ and x₂ are the successive values of the amplitude on the same side of the mean position, then the logarithmic decrement is equal to

log(x₁.x₂)
loge(x₁/x₂)
log(x₁/x₂)
x₁/x₂

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

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

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