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Cylinder floating

  1. Mar 12, 2013 #1
    Hi everyone,
    I have an exercise and i don't understand something in the solution:
    A cylinder of diameter d floats with l of its length submerged. The total height is L. Assume no
    damping. At time t = 0 the cylinder is pushed down a distance B and released.
    What is the frequency of oscillation?

    The diameter of the floating cylinder is d and it has l of its length submerged in water. The volume of water
    displaced by the submerged part of the cylinder in equilibrium condition is πd2l/4. Let the density of water be ρ
    and the density of cylinder be ρcyl. Hence the mass of the cylinder is:
    Mcyl = ρw*Vdisplaced= ρw*πd2l/4=ρcyl*πd2L/4
    Frestoringw*gπd2x/4
    Mcylx"=ρw*gπd2x/4
    w²=ρw*gπd2/4Mcyl
    w²=g/l

    Why are they taking Vdisplaced=πd2l/4 Why /4 ???
    And why l is equa to 4Mcylw*πd2

    Thanks !
     
  2. jcsd
  3. Mar 12, 2013 #2

    TSny

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    Gold Member

    What's the formula for the area of a circle expressed in terms of its diameter (not radius)?
    This relationship comes from the first equation you wrote.
     
  4. Mar 12, 2013 #3
    Oh okey i didn't notice that it was written in terms of the diameter !
    Thanks !

    I have another question about oscillations, it was an assignment that we did two weeks ago. I didn't understand the exercise so I didn't do it and my teacher doesn't give the details of the solutions. I'm expecting someone to help me and explain me the steps:

    Three block of mass m=0.13kg are connected with three springs of constant k1 k2 k3 and

    Two of the normal modes of the system, expressed in terms of displacement are :
    |1>=( 1 0 -3) |2>= ( 27 -10 9)

    Knowing that the lower frequency that isn't necessarly the first mode frequency is 20 rad/s. Find the spring constants.

    All i did is that i gave the equations of motion so i got few points for that, and found the |3> as they're perpendicular between them.

    Thank you, I have an exam tomorrow and need to understand this !
     
  5. Mar 12, 2013 #4

    TSny

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    I think you should post this as a separate question with an appropriate title.
     
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