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DHM equation

  1. Feb 21, 2008 #1
    Concerning damped harmonic motion (eg. mass on a spring, using cardboard discs as dampers); for the equation (below) of the graph describing the effect of different sized dampers on the time taken for amplitude of oscillations to halve, what would b (y-intercept) and n (gradient) represent? (A=area of damper; T=time taken for amplitude to halve)

    [tex]T=b.A^n[/tex]
    [tex]ln(T)=n.ln(A) + ln(b)[/tex]

    Thanks
     
  2. jcsd
  3. Feb 21, 2008 #2

    Andy Resnick

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    Blech... I vaguely recall this stuff from a control engineering class.

    Wikipedia has some useful background:
    http://en.wikipedia.org/wiki/Damping

    What helps me is to consider limiting cases- the area of the damper going to zero, or infinity, for example. Let's first consider a damper of unit area: A^n is always 1 then. Then b is linearly related to the 'damping time', and is probably connected to the 'damping ratio' of a damped oscillator.

    That leaves 'n', which is the effect of varying the area of the damper. Question- how does varying the area change the damping time? is it a linear relationship (n=1)? nonlinear (n>1)? sublinear (n<1)? I don't know the answer, but that's what 'n' represents.
     
  4. Feb 25, 2008 #3
    Thanks for the reply!

    Now, I have a value for both constants, and both a graph of T against A and one of log(T) against log(A). This is for coursework, and having neglected to find spring constant k or any other potentially useful information, Im having trouble making my interpretation and conclusions 'worthwhile'- other than stating vague implications of the values of b and n. With the data I have would it be possible to find a complete equation for the motion of the spring? Thanks
     
  5. Feb 26, 2008 #4

    Andy Resnick

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    Well, you may be able to figure out actual values for 'n' and 'b'... What exactly is the purpose of the lab?
     
  6. Feb 26, 2008 #5
    I have values but without n and b directly representing anything physical I'm finding it hard to go very in-depth in analysis; for alevel coursework I think more than just a few lines would be needed. The aim was to investigate the effect of damping on SHM of a spring-mass system- I left it vague because at the time didn't know how I would go about it
     
  7. Feb 26, 2008 #6

    Andy Resnick

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    Oh. That's a different question than what you initially asked, I think. How did you arrive at the equation in your original post? Was it given to you, or did you guess using Excel or something?
     
  8. Feb 26, 2008 #7
    It was given to me, as an equation for the graph. Initially I though b and n would represent something physical, but it seems they don't, at least not directly - eg. you said b would be connected to the damping coefficient, but without knowing how I can't write much on it.
     
  9. Feb 28, 2008 #8

    Andy Resnick

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    Hmmm.. Well, when I get ambiguous comments from reviewers, my strategy is to first re-state the comment as best I can in terms that I do understand, and then provide a response. Sometimes that works, sometimes it doesn't.

    So, think about how the damping occurs in your system- demonstrate you understand a damped oscillator. Then, think about what a power-law (T ~ A^n) means physically- that would be impressive to talk about- and then try and relate the two. For example- the area of the disk is related to the mass of the damper, and so is related to 'b' as well: can you re-write the power law in terms of the mass of the damper?
     
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