In practice, it is often difficult to determine the

Chapter 19, Problem 19.130

(choose chapter or problem)

In practice, it is often difficult to determine the logarithmic decrement of a system with light damping defined in Prob. 19.129 by measuring two successive maximum displacements. Show that the logarithmic decrement can also be expressed as \((1 / k) \ \ln \left(x_{n} / x_{n+k}\right)\), where k is the number of cycles between readings of the maximum displacement.

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