Question

The damping ratio is

• A. 0.274
• B. 0.256
• C. 0.263
• D. 0.232

Answer 1

Answer: (D)

0.232

For successive amplitudes $m=2$
amplitude reduction factor
$=ln\left(\frac{x_1}{x_2}\right)=ln\left(\frac{100}{5}\right)=ln20=2.996$
amplitude reduction factor $=\frac{2\pi \delta m}{\sqrt{1-{\delta }^2}}$
$\Rightarrow \frac{2\pi \delta m}{\sqrt{1-{\delta }^2}}=2.996$
squaring both sides
$\frac{4{\pi }^2{m}^2{\delta }^2}{1-{\delta }^2}=8.967\Rightarrow \frac{157.9{\delta }^2}{1-{\delta }^2}=8.967\Rightarrow {\delta }^2=0.0538\Rightarrow \delta =0.232$