Question

A vibrating system is analysed and it is found that two successive oscillations have amplitudes of $3$ mm and $0.5$ mm respectively. Calculate the damping ratio.

• A. $0.274$
• B. $0.256$
• C. $0.263$
• D. $0.292$

Answer 1

The correct option is A $0.274$

For successive amplitudes $m=1$
Amplitude reduction factor $=ln\left(\frac{x_1}{x_2}\right)=ln\left(\frac{3}{0.5}\right)=ln6=1.792$
Amplitude reduction factor $=\frac{2\pi \delta m}{\sqrt{1-{\delta }^2}}$
$\Rightarrow \frac{2\pi \delta m}{\sqrt{1-{\delta }^2}}=1.792$
squaring both sides
$\frac{39.478{\delta }^2}{1-{\delta }^2}=3.21\Rightarrow {\delta }^2=0.075\Rightarrow \delta =0.274$