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Damping and resonance

  1. Mar 29, 2017 #1
    1. The problem statement, all variables and given/known data

    x''+b*x'+k*x=k*y+b*y' y=cos(omega*t)

    k is fixed, b - damping constant slowly increases.

    How does increasing the damping constant b affect the resonance peak?

    2. The attempt at a solution

    Well, I thought the answers:
    It significantly decreases the height of the resonant peak.
    and
    It significantly decreases the frequency at which resonance happens.
    are correct.

    I have found a useful resource - http://physicsnet.co.uk/a-level-physics-as-a2/further-mechanics/forced-vibrations-resonance/

    But these answers were marked as wrong. I have no idea why. What have I missed? Is it possible that this option is correct: It does not significantly change the shape nor the location of the resonance peak.?
     
  2. jcsd
  3. Mar 29, 2017 #2

    Orodruin

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    Normally when you consider damping you assume the amplitude of the driving force to be fixed. In this case, you should note that your driving force depends on and increases with b. Think about how that will change the behaviour of the system.
     
  4. Mar 29, 2017 #3

    BvU

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    This the literally rendered problem statement ? Why the funny expression on the righthand side ?
     
  5. Mar 29, 2017 #4

    Orodruin

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    I suspect there is a comma missing between y' and y.
     
  6. Mar 30, 2017 #5
    Yes, a comma is missing. :( There is also a mathlet but of course I can't copy it.

    I have got it right eventually. :)

    Many thanks. :)
     
  7. Mar 30, 2017 #6

    BvU

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    I suspect the idea is to look at x''+b*x'+k*x=y
    with y=cos(omega*t)
     
  8. Mar 30, 2017 #7
    Yes, exactly. You can also adjust omega with the mathlet.
     
  9. Mar 30, 2017 #8

    Orodruin

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    I strongly suspect that this is not the case and that the problem indeed wants a derivative of ##y## on the right-hand side along with the quoted constants, i.e.,
    $$
    x'' + b x' + kx = k \cos(\omega t) - b \omega \sin(\omega t).
    $$
     
  10. Mar 30, 2017 #9

    BvU

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    Which would be relevant if ##b## is time dependent. Am I to interpret
    as "find the steady state solution with ##b## constant and look at how the resonance peak depends on ##b## "?
     
  11. Mar 30, 2017 #10

    Orodruin

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    That is how I would interpret it.
     
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