= Minimum phase speed of a flexural-gravity wave
{title2=$c_{p,\min}=\min_{k>0}\omega(k)/k$}
Write $\beta=D/\rho_w$ and $\alpha=m/\rho_w$ in the <dispersion relation of a floating elastic plate>. A stationary point of squared <phase velocity> satisfies $\beta k^4(3+2\alpha k)=g(1+2\alpha k)$. If plate inertia is neglected, its solution is $k=(g/(3\beta))^{1/4}$. A steadily translating load can resonate only when its speed matches a <phase velocity>; this threshold differs from the <group-velocity minimum of a flexural-gravity wave>.
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