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

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

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Theory of Machine
When the belt is stationary, it is subjected to some tension known as initial tension. The value of this tension is equal to the

Average tension of the tight side and slack side of the belt
Tension in the tight side of the belt
Sum of the tensions on the tight side and slack side of the belt
Tension in the slack side of the belt

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