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Oscillations: Damped Block

  1. Jun 16, 2011 #1
    1. The problem statement, all variables and given/known data
    The drawing to the left shows a mass m= 1.8 kg hanging from a spring with spring constant k = 7 N/m. The mass is also attached to a paddle which is emersed in a tank of water with a total depth of 27 cm. When the mass oscillates, the paddle acts as a damping force given by -b(dx/dt) where b= 270 g/sec. Suppose the mass is pulled down a distance 1.1 cm and released.

    a) What is the time required for the amplitude of the resulting oscillations to fall to one third of its initial value?
    ΔT = 14.64816 sec

    b) How many oscillations are made by the block in this time?
    ????????
    2. Relevant equations

    [tex]A(t)=A(0)e^{-bt/2m}[/tex]
    ???

    3. The attempt at a solution
    I solved part a) and the computer verified my answer so I know its correct. I am just stuck on part b. I think I need to somehow find the period and then take the time in a) and divide it by the period. My book is confusing and I am not sure which equation to use.


    EDIT: Finally found equation for period. It was T= 2pi sqrt (k/m) and then I took my answer from a) and divided it by the period to get the answer.
     
    Last edited: Jun 16, 2011
  2. jcsd
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