- #1

- 69

- 0

[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.