Divide the equation by m and compare its left side with $\ddot x+2\zeta\omega_n\dot x+\omega_n^2x$. Since $\omega_n=\sqrt{k/m}$ and $2\zeta\omega_n=c/m$, we get $\zeta=c/[2\sqrt{km}]$. This dimensionless ratio is option B.
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