= Critical gravity-tunnel settling time
{title2=$b_c=2m\omega_0,\quad y/y_s=(1+\omega_0t)e^{-\omega_0t}$}
Adding a velocity-proportional <force> $-b\dot y$ produces a <damped harmonic oscillator>. The fastest non-oscillatory release from rest is critical <damping>, with the repeated-root solution in the title. Reaching fraction $\varepsilon$ of the initial displacement requires $(1+s)e^{-s}=\varepsilon$, $s=\omega_0t$. At one percent, $s=6.638352\ldots$, rather than $\log100$. Exact arrival at equilibrium takes infinite time; the tolerance reference must be stated.
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