1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Approximation of string extension length

  1. Apr 5, 2012 #1
    1. The problem statement, all variables and given/known data

    A string of length a is stretched to a height of y when it is attached to the origin so making a triangle with length L=[itex]\sqrt{a^{2}+\frac{y^{2}}{a^{2}}}[/itex] and therefore a length extension ΔL= [itex]\sqrt{a^{2}+\frac{y^{2}}{a^{2}}}-a[/itex] which simplifies to [itex]{a(\sqrt{1+\frac{y}{a}^{2}}-1}[\itex].

    Apparently when the displacement y is small, it can be approximated to y^2/2a

    How does that even work??
  2. jcsd
  3. Apr 5, 2012 #2
    Are you sure you got the result right? Seems to me like there should be a³, not a. This works by a method called Taylor's series. You can read about it in wikipedia: http://en.wikipedia.org/wiki/Taylor_series
  4. Apr 5, 2012 #3
    Ah of course. I'm familiar with Taylor but I just didn't apply it. However, I've just done it and it is over 2a. Thanks for pointing me down the right track! :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook