Question

A single degree of freedom mass-spring-viscous damper system with mass m, spring constant k and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is

• A. $q=\sqrt{2km}$
• B. $q=2\sqrt{km}$
• C. $q=\sqrt{\frac{2k}{m}}$
• D. $q=2\sqrt{\frac{k}{m}}$

Answer 1

The correct option is B $q=2\sqrt{km}$

Given,

1. Single degree of freedom
2. Mass = m
3. Spring constant = k
4. Damping coefficient = q
5. Critically damped

Damping factor = 1


Correct relation :

$\text{Damping factor}=\frac{\text{Damping coefficient}}{2\times \text{Mass}\times \text{Natural frequency of vibration}}$

$1=\frac{q}{2\times m\times \sqrt{\frac{k}{m}}}$

$q=2\sqrt{km}$