On the virtual-mass and damping coefficients for long waves in water of finite depth

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Abstract
A half-immersed circular cylinder is making vertical oscillations on water of finite constant depth. The virtual-mass and damping coefficients are studied in the limit as the wavelength tends to infinity. It is found that the virtual-mass coefficient tends to a finite limit and that the amplitude ratio ultimately varies as the frequency. This behaviour differs from the behaviour for infinite depth, where the virtual-mass coefficient tends to infinity and the amplitude ratio ultimately varies as (frequency).

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