Question

A mass of 5 kg is suspended from a spring of stiffness 46 kN/m. A dashpot is fitted between the mass and the support with a damping ratio of 0.3. Calculate the damped frequency.

• A. 14.56 Hz
• B. 14.28 Hz
• C. 14.42 Hz
• D. 14.14 Hz

Answer 1

The correct option is A 14.56 Hz

The natural undamped frequency is given by
$f_n=\frac{1}{2\pi }\sqrt{\frac{k}{M}}\Rightarrow f_n=\frac{1}{2\pi }\sqrt{\frac{46000}{5}}=15.26Hz$
The damped frequency is given by
$f=f_n\sqrt{1-{\delta }^2}=15.26\times \sqrt{1-0.09}=14.56Hz$