Question

The damping ratio for a viscously damped spring mass system, governed by the relationship $m\frac{d^{2}x}{d{t}^2}+c\frac{dx}{dt}+kx=F\left(t\right)$, is given by

• A. $\sqrt{\frac{c}{mk}}$
• B. $\frac{c}{2\sqrt{km}}$
• C. $\frac{c}{\sqrt{km}}$
• D. $\sqrt{\frac{c}{2\sqrt{km}}}$

Answer 1

The correct option is B $\frac{c}{2\sqrt{km}}$

We know that:

$2\xi {\omega }_n=\frac{c}{m}$

$\xi =\frac{c}{m\times 2{\omega }_n}=\frac{c}{2m\sqrt{\frac{k}{m}}}=\frac{c}{2\sqrt{km}}$