Question

A mass of 30 kg is supported on a spring of stiffness 60000 N/m. The system is damped and the damping ratio is 0.4. The mass is raised 5 mm and then released. Calculate the damped frequency in Hz.

• A. 6.235
• B. 6.352
• C. 6.523
• D. 6.325

Answer 1

The correct option is C 6.523

The natural frequency is given by
$f_n=\frac{1}{2\pi }\sqrt{\frac{k}{M}}\Rightarrow f_n=\frac{1}{2\pi }\sqrt{\frac{60000}{30}}=7.118Hz$
The damped frequency is given by
$f=f_n\sqrt{1-{\delta }^2}=7.118\times \sqrt{1-0.16}=6.523Hz$