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Homework Help: Deriving differential eqaution

  1. Mar 28, 2005 #1
    I am trying to derive an equation for the oscillation of a conical float. There is a conical float with a density of delta 2 and its floating on water with density 1. Find the oscillation of the floating conical float. The final solution should be:
    d^2y/dt^2=-g+(g((L-y)/L)^3)/p

    where y(t) is the height of the conical float over the water, L is the length of the conical float,g is gravity and p is the ratio of the two density delta1/delta2

    what i did was i found the submerge volume: (1/3)r^2(L-y)

    then the weight of water displaced by the float is:
    (1/3)r^2(L-y)*delta2*g

    mass of float m=(1/3)r^2(L)*delta2

    using this in newton's second law i got:
    d^2y/dt^2=-g+g*p((L-y)/L) where p=delta1/delta2

    i am not getting the solution that my professor gave?...can somebody explain where the cubed part came from?
     
  2. jcsd
  3. Mar 29, 2005 #2

    ehild

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    Homework Helper

    use delta1 instead of delta2.

    You can not use the same r for both parts. If R is the radius of the base of the whole conus and r is the same for the submerged part, r/R=(L-y)/L

    ehild
     
  4. Mar 29, 2005 #3
    You would need at least to show that

    [tex]\frac{d^2y}{dt^2} = ky[/tex]

    Also I believe you have to clarify whether the cone is upside down, or with the base down.
     
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