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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??

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# Homework Help: Approximation of string extension length

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