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Transverse Displacement of Stretched String: Derivation of Poisson Eq.

  1. May 22, 2009 #1

    UAR

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    Please how would one derive the Poisson Equation model,

    [tex]\nabla^{2}\psi(x) = \frac{F(x)}{T}[/tex],

    for Transverse displacement [tex]\psi(x)[/tex] of a stretched string under constant non-zero tension T and an externally applied transverse force F(x) . Assuming small angle with the horizontal (i.e [tex]sin(\theta)\approx\theta[/tex]) ?

    Thanks
     
    Last edited: May 22, 2009
  2. jcsd
  3. May 22, 2009 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    Start by by drawing a picture and labeling all the forces acting on the string. Then apply Newton's second law.
     
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