Transverse Displacement of Stretched String: Derivation of Poisson Eq.

  • Thread starter UAR
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  • #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
 
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Answers and Replies

  • #2
gabbagabbahey
Homework Helper
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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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