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Resonance of a pressure-forced rectangular surface-gravity mode

Pressure forcing of one rectangular free-surface mode reduces its amplitude to

H^{''} + g k H = - \frac{k p _{0}}{ρ} cos (ω t) .

At

ω = g k

, the inviscid undamped response contains

t sin (ω t)

and grows without bound in the linear model.

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