Question

A mass of 5 kg is suspended from a spring of stiffness 4000 N/m. The system is fitted with a damper with a damping ratio of 0.2. The mass is pulled down 50 mm and then released. Calculate the damped frequency.

• A. 4 Hz
• B. 4.41 Hz
• C. 5 Hz
• D. 5.52 Hz

Answer 1

Answer: (B)

4.41 Hz

The natural frequency is given by
$f_n=\frac{1}{2\pi }\sqrt{\frac{k}{M}}\Rightarrow f_n=\frac{1}{2\pi }\sqrt{\frac{4000}{5}}=4.5Hz$
The damped frequency is given by
$f=f_n\sqrt{1-{\delta }^2}=4.5\times \sqrt{1-0.04}=4.41Hz$