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A vibration system consists of a mass of 175 kg, a spring stiffness 700 N/cm and damper with a damping coefficient of 7 Ncm-1sec. Damping factor of the system is:


1. 0.15
2. 0.25
3. 0.2
4. 0.1

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Correct Answer - Option 4 : 0.1

Concept:

Free damped Vibration:

\(m\frac{{{d^2}x}}{{d{t^2}}} + c\frac{{dx}}{{dt}} + kx = 0\)

\(m\ddot x + c\dot x + kx = 0\)

Natural frequency:

\({\omega _n} = \sqrt {\frac{k}{m}}\)

Damping factor:

\(ξ = \frac{c}{{{c_c}}} = \frac{c}{{2\sqrt {km} }} \)

Where c = damping coefficient , m = mass, k = spring stiffness.

Calculation:

Given:

m = 175 kg, k = 700 N/cm = 70000 N/m , c = 7 Ncm-1sec = 700 Nm-1sec

\(ξ = \frac{c}{{{c_c}}} = \frac{c}{{2\sqrt {km} }} \)

\(ξ = \frac{c}{{2\sqrt {km} }} \)

\(ξ = \frac{700}{{2\sqrt {70000\times175} }} =0.1\)

ξ = 0.1

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