= Viscously damped U-tube oscillation
{title2=$\Gamma=\beta/(\rho A)$}
If resisting <force> per unit moving length is $\beta v$, the total resistance is $\beta l\dot y$ and $\ddot y+\Gamma\dot y+\omega_0^2y=0$, where $\Gamma=\beta/(\rho A)$. For $\Gamma<2\omega_0$, an initial <velocity> $v_0$ from zero displacement gives $y=(v_0/\omega_d)e^{-\Gamma t/2}\sin\omega_dt$, with $\omega_d^2=\omega_0^2-\Gamma^2/4$. Its quality parameter is $Q=\omega_0/\Gamma$, and the <amplitude> envelope decays at half the energy-decay exponent. The effective <damping> model is an assumption, not a derivation of detailed viscous flow near the wall.
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