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Damped Harmonic Oscillator

  1. Dec 8, 2016 #1
    1. The problem statement, all variables and given/known data
    A damped harmonic oscillator consists of a block (m = 2.72 kg), a spring (k = 10.3 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.5 cm; because of the damping, the amplitude falls to 0.721 of the initial value at the completion of 7 oscillations. (a) What is the value of b? (Hint: Assume that b2 << km.) (b) How much energy has been lost during these 7 oscillations?


    2. Relevant equations


    3. The attempt at a solution
    so first to find the period
    T=2pi(m/k)^0.5
    =2pi(2.72kg/10.3N/m)^0.5
    =3.23 seconds
    I know that this will be used in finding b, along with the mass, but I am clueless where to go from here. Part b was much easier to figure out with the energy lost being 0.2 J
     
  2. jcsd
  3. Dec 8, 2016 #2
    I know the equation is (2m*ln(x))/(T*oscillations). Is the ln(x)=ln(1/%of energy retained)?
     
  4. Dec 8, 2016 #3

    rude man

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    Gold Member

    That is not the period of the oscillations. (It would be if b=0).
     
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