Question

A spring-mass-damper system having single degree of freedom has a spring with strength 25 kN/m, mass 0.1 kg and coefficient of damping 40 N-s/m. The damping factor of the system will be
1. 0.32
2. 0.5
3. 0.4
4. 0.64

Answer 1

Correct Answer - Option 3 : 0.4

Concept:

The damping ratio (ξ) is defined as ratio of viscous damping coefficient to critical viscous damping coefficient.

\(⇒ {{ξ }} = \frac{{{c}}}{{2\sqrt {{{km}}} }}{{\;\;\;\;\;}} \ldots \left( 1 \right)\)

Where, ξ = damping ratio, c = damping coefficient, k = spring constant, 

Calculation: 

Given: 

m = 0.1 kg, k = 25 kN/m, c = 40 Ns/m

Using equation (1),

\(⇒ {{ξ }} = \frac{{40}}{{2\sqrt {25 \times 10^3\times 0.1} }}{{}}\)

⇒ ξ = 0.4