A vibrating system consists of a mass of 200 kg and a spring of stiffness 80 N/mm. The circular frequency of un-damped vibration is:

Question

Question

This question was previously asked in

BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

The circular frequency (natural frequency in rad/s) for undamped free vibrations is given by:

\( \omega_n = \sqrt{\frac{k}{m}} \)

Where,

Given:

Mass, \( m = 200~\text{kg} \)

Stiffness, \( k = 80~\text{N/mm} = 80 \times 10^3~\text{N/m} \)

Calculation:

\( \omega_n = \sqrt{\frac{80 \times 10^3}{200}} = \sqrt{400} = 20~\text{rad/s} \)