Question

A vibrating system consists of a mass of 100 kg, a spring of stiffness 50 kN/m and a damper. The damper provided is only 10% of the critical value.

The natural frequency of damped vibrations is

• A. 22.25 rad/s
• B. 22.36 rad/s
• C. 43.8 rad/s
• D. 44.72 rad/s

Answer 1

The correct option is A 22.25 rad/s

${\omega }_d={\omega }_n\sqrt{1-{\xi }^2}$

${\omega }_n\sqrt{\frac{k}{m}}=\sqrt{\frac{50\times {10}^3}{100}}=22.36\text{rad/s}$

${\omega }_d=\left(22.36\right)\times \sqrt{(1-(0.1{)}^2)}$

$=22.25\text{rad/s}$