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In a spring-mass system, the mass is m and the spring constant is k. The critical damping coefficient of the system is 0.1kg/s. In another spring-mass system, the mass is 2m and the spring constant is 8k. The critical damping coefficient (in kg/s) of this system is __________

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Concept:

For a Damped free vibration,

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

where, ζ is damping factor, C is damping coefficient and Cc is critical damping coefficient.

when ζ =1, c = cc = 2√(km)   

Calculation:

Given, cc1 = 0.1 kg/s, m2 = 2m and k2 = 8k

\({c_{c1}} = 2\sqrt {{k_1}{m_1}} = 2\sqrt {km}\)

\({c_{c2}} = 2\sqrt {{k_2}{m_2}} = 2\sqrt {8k \times 2m} = 4{c_{c1}} = 4 \times 0.1 = 0.4\) kg/s.

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