Find the period of the motion . · OlympiadBench #1502

Physics · thermodynamics

Problem

Find the period of the motion TT. Neglect the viscosity of the liquid. Given constants: A solid, uniform cylinder of height h=10 cmh=10 \mathrm{~cm} and base area s=100 cm2s=100 \mathrm{~cm}^{2} floats in a cylindrical beaker of height H=20 cmH=20 \mathrm{~cm} and inner bottom area S=102 cm2S=102 \mathrm{~cm}^{2} filled with a liquid. The ratio between the density of the cylinder and that of the liquid is γ=0.70\gamma=0.70. The bottom of the cylinder is above the bottom of the beaker by a few centimeters. The cylinder is oscillating vertically, so that its axis always coincides with that of the beaker. The amplitude of the liquid level oscillations is A=1 mmA=1 \mathrm{~mm}.

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