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Brad23
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Homework Statement
A body of uniform cross-sectional area A and mass density [itex]\rho[/itex] floats in a liquid of density [itex]\rho_0[/itex] (where [itex]\rho < \rho_0[/itex]), and at equilibrium displaces a volume [itex]V[/itex]. Making use of Archimedes principle (that the buoyancy force actign on a partially submerged body is equal to the mass of the displaced liquid), show that the period of small amplitude oscillations about the equilibrium position is:
[itex]T = 2\pi \sqrt{\frac{V}{gA}}[/itex]
Homework Equations
[itex]F_{buoyancy} = mg[/itex]
[itex]\ddot{x} = -\omega^2 x[/itex]
[itex]T = \frac{2\pi}{\omega}[/itex]
The Attempt at a Solution
I feel like that is my starting point, but I can't seem to set of the differential equation in order to solve for something to get me to the period