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Eric_meyers
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Homework Statement
A body of uniform cross-sectional area A and mass density ρ floats in a liquid
of density ρ0 (where ρ < ρ0), and at equilibrium displaces a volume V.
Making use of Archimedes principle (that the buoyancy force acting 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
T = 2(pi)[tex]\sqrt{V/(gA)}[/tex]
Homework Equations
fnet = mg - p0*V*g
The Attempt at a Solution
Ok, I wanted to set up a differential equation.
ma + p0*V*g - mg = 0
or
m * x'' + p0*V*g - mg = 0
however, I know this not to be the right equation because I'm missing an "x" term to make this solvable.
so then I went another way
ma = g(m-p0V)
a = g - p0*V/m
but a = -(z)*w^2 ; z = amplitude
and
p0*V/m = 1
---------------------
-(z)*w^2 = g - 1
(z)*w^2 = 1 - g
w^2 = (1-g)/z
w = [tex]\sqrt{(1-g)/z}[/tex]
and then T = 2(pi) / w
but this isn't the right answer :(