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Homework Help: Damped Forced Harmonic Oscillations

  1. May 9, 2010 #1
    1. The problem statement, all variables and given/known data
    If F0= 0 and γ<<2ω0 where γ=b/m, sketch the resulting wave-form for displacement with time.Define Q,the quality parameter,and show on your sketch how the value of Q, influences the waveform



    2. Relevant equations
    mψ'' =-kψ-bψ' +F0exp(-iωt)


    3. The attempt at a solution
    ωmax=(ω0-γ^2/2)^(1/2)
    if γ <<2ω0 then ωmax=ω0,
    An other question is :Is the graph enought to define Q? ,i.e at resonance F0/k is Q times more.
     

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  3. May 9, 2010 #2

    vela

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    You're not doing what the problem asked, which is to sketch x(t) vs. t. What kind of behavior do you get from this oscillator knowing that ϒ<<2ω0 and F0=0?
     
  4. May 9, 2010 #3
    mψ'' =-kψ-bψ' +F0exp(-iωt)

    If we devide the equation by m we get :
    ψ''+ω0^2ψ+γψ'+F0exp(-iωt)=0 This is the most general equation for oscillations , (since γ=b/m and ω0=k/m)
    So you are actualy saying that Since F0 is zero ,there is no external force#
    and since γ<<2ω0 ,then approximately the term γψ' is also zero ,therefore additionally there is no damping
    and therefore we have Simple Harmonic motion ?
     
  5. May 9, 2010 #4

    vela

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    Your original post said F0=0, so there's no driving force continually adding energy to the system. The problem wants you to show how the system evolves after an initial impulse is imparted to get it moving. Don't assume no damping, however.
     
  6. May 9, 2010 #5
    Ok thanks ,problem solved it is light damping, i was looking for other cases...
     
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