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Damping constant and angular frequency

  1. Nov 3, 2011 #1
    While discussing [itex]ω^{'}[/itex], the angular frequency of a damped harmonic oscillator, given by:
    [itex]ω^{'}=\sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}}}[/itex]
    where k is the "springiness", m is the mass, and b is the damping constant,
    my book, Halliday, Resnick and Walker, says if b is small but not zero,[itex]b<<\sqrt{km}[/itex] then [itex]ω^{'}\approxω[/itex]. [itex]ω=\frac{k}{m}[/itex], the undamped frequency.

    If I say that [itex]\frac{k}{m}>>\frac{b^{2}}{4m^{2}}[/itex]and go through the algebra to get the relation in the book, I get [itex]b<<\sqrt{2km}[/itex]
    Is this a meaningful difference when talking about a quantity that is much, much less than another?
    Thanks for any help.
     
  2. jcsd
  3. Nov 3, 2011 #2

    Redbelly98

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    The two statements, [itex]b \ll \sqrt{km} \text{ and } b \ll \sqrt{2km}[/itex], are essentially considered to be equivalent statements.
     
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