Question

A rod vibrates with a frequency of 2 Hz when there is no damping. If the damping is provided, the frequency of damped vibration was observed to be 1 Hz. The logarithmic decrement is

• A. 10.88
• B. 6.82
• C. 4.28
• D. 2.82

Answer 1

The correct option is A 10.88

$f_n=2Hz,f_d=1Hz$
Natural frequency of undamped vibration
${\omega }_n=2\pi f_n=2\pi \times 2=4\pi rad/s$
Natural frequency of damped vibration,
${\omega }_d=2\times \pi \times 1=2\pi rad/s{\omega }_d={\omega }_a\sqrt{1-{\xi }^2}2\pi =4\pi \sqrt{1-{\xi }^2}\Rightarrow \xi =0.866$
Logarithmic decrement, $\delta =\frac{2\pi \xi }{\sqrt{1-{\xi }^2}}=\frac{2\times \pi \times 0.866}{\sqrt{1-{0.866}^2}}=10.88$