Question

Consider the displacement vs time graph for a damped natural vibration system shown below;

The damping factor is ?

• A. 0.25
• B. 0.04
• C. 0.02
• D. 0.30

Answer 1

The correct option is B 0.04


$\delta =\text{ln}\left(\frac{x_n}{x_{n+1}}\right)=\text{ln}\left(\frac{90}{70}\right)$

$\delta =0.2513$

$and\delta =\frac{2\pi \xi }{\sqrt{1-{\xi }^2}}$

$put{\xi }^2=X$

$\delta =\frac{2\pi \sqrt{X}}{\sqrt{1-X}}$

${\delta }^2=\frac{4{\pi }^{2}X}{1-X}$

$\Rightarrow {0.2513}^2(1-X)=4{\pi }^{2}X$

$0.063-0.063X=4{\pi }^{2}X$


$0.063=30.54X$

$\Rightarrow X=1.59\times {10}^{-3}$

$\xi =\sqrt{X}$

$\xi =0.0399\simeq 0.040$