= Practical damping choice
To settle quickly after loading, <critical damping> is preferable to the supplied weak damper:
$$
\boxed{b_c=2\sqrt{k(m+M)}\simeq1.44\times10^4\,\mathrm{N\,s\,m^{-1}}}.
$$
Using the strict-bound <mass> instead changes this by less than $1\%$. This eliminates free ringing while avoiding the slow tail of severe <overdamping>. In the stipulated external-force model, greater damping also reduces the steady forced amplitude; there is no finite optimum based solely on that amplitude. A critical or near-critical value is a practical compromise for rapid settling. If the disturbance were specified as floor displacement transmitted through the legs, damping would introduce an additional transmission tradeoff, but that is a different forcing model.
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