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Homework Help: Density and simple harmonic motion

  1. Jan 21, 2007 #1
    1. The problem statement, all variables and given/known data
    A mass of density d floats in a liquid of density d_L. The mass is then pushed down a distance x and let go. Use Newton's Second Law to demonstrate that the mass will undergo simple harmonic motion. Recall that the SHM equation is d^2x/dt^2 + w^2*x = 0. Assume there is no friction. Find w in terms of whatever variables needed.


    2. Relevant equations



    3. The attempt at a solution

    I know that Newton's 2nd law is sum F=ma, and Torque = I*omega. I don't see how I can relate this to simple harmonic motion, which involves things moving back and forth in the same pattern. The answer key says that w=SQRT(D_l * g/(D*H)). However, I don't know what I am missing to solve this problem. I don't know where to start.
     
  2. jcsd
  3. Jan 21, 2007 #2
    I think a free body diagram would be a good place to start. Then I would use Newton's second law. Torque, huh?
     
  4. Jan 21, 2007 #3
    When the object is at rest, I have mg pulling down and buoyant force pushing up. They are equal in magnitude. The net torque is also zero.

    When the object is pushed down I have f pushing down, mg pulling down, and buoyant force pushing up. This extra f is enough to push it down. My net torque is

    T = IW

    However, why would I use this? Isn't torque normally used when things are rotated?

    T = F x R

    What R in this case? Mg and buoyant are both pushing from the center in the free body diagram so I don't think there is an R. So f is the only force that contributes to the torque am I correct?
     
  5. Jan 21, 2007 #4
    Torque shouldn't come into play. You've listed some forces, now put them into equations.
     
  6. Jan 21, 2007 #5
    For the object at rest

    I got

    B - mg = 0

    When it's pushed down

    B - mg -f = -ma

    Since B =mg

    f = ma

    I already know this though so how does it help prove that it's in simple harmonic motion with a repeating pattern?
     
  7. Jan 21, 2007 #6
    Never mind I got it now. Thanks a lot for your help.
     
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