# This problem investigates the number of cycles (n) re- quired for a structural oscillation amplitude to decay

## Question:

This problem investigates the number of cycles \(n\) re-

quired for a structural oscillation amplitude to decay to \(x \%\) of its maximum.

**(a)** What is the expression for the logarithmic decrement in terms of \(n\) and \(x\) ?

**(b)** Solve for \(n\) in terms of \(\zeta\) and \(x\).

**(c)** Plot \(n\) as a function of \(\zeta\) for (i) \(x=70 \%\), (ii) \(x=50 \%\), (iii) \(x=20 \%\) using the exact formula, and then using the approximate formula for \(\zeta=0.1\) and \(\zeta=0.5\).

## Step by Step Answer:

**Related Book For**

## Mechanical Vibration Analysis, Uncertainties, And Control

**ISBN:** 9781498753012

4th Edition

**Authors:** Haym Benaroya, Mark L Nagurka, Seon Mi Han