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.