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Leaky bucket in SHM

  1. Aug 13, 2013 #1
    1. The problem statement, all variables and given/known data
    There is a bucket with a leak in it in verticle SHM. What is the rate that the period changes with time?
    dm/dt = 2 g/s
    bucket = 2 kg
    total water = 10kg
    starting amplitude = 3cm
    k=125 N/m


    2. Relevant equations
    T=2pi*sqrt(m/k)



    3. The attempt at a solution

    dT/dt = 2pi * sqrt((dm/dt)/k)
    dT/dt = 2pi * (dm/dt)^1/2 / k^(1/2)
    dT/dt = 2pi * (m/2)^-1/2 / k^1/2
    dT/dt = 2pi * (m2k)^-1/2

    my calculus isn't the sharpest so I probably screwed up taking the derivative?
     
  2. jcsd
  3. Aug 13, 2013 #2
    Yeah, I think you did. Take a look at the first line again. You clearly know ##\sqrt{A}=A^{\frac{1}{2}}##, so perhaps make that conversion for ##T## before taking the derivative. Also, you will need the chain rule for this problem.
     
  4. Aug 13, 2013 #3

    rude man

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    What does this mean? Units have to be kg/s, not g/s.
     
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