Question

In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original value. What is the damping coefficient of the damper?

• A. 1.2 Ns/m
• B. 3.4 Ns/m
• C. 8.7 Ns/m
• D. 12.0 Ns/m

Answer 1

The correct option is C 8.7 Ns/m

Given
${\omega }_d=0.9{\omega }_n$

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

$\Rightarrow 0.9{\omega }_n={\omega }_n\sqrt{1-{\xi }^2}$

$\therefore$ $\xi =0.436$

Now $\xi =\frac{c}{2\sqrt{km}}$

$\therefore$ $c=2\times 0.436\times \sqrt{1000\times 0.1}$

$=8.71$ Ns/m