5. For a string under tension, small displacements y(x) due to a static force f(x) satisfy -y"(x) = f(x). For fixed boundary conditions y(x = 0) = 0 and y(x = 1) = 0, the Green's function for a delta function force 8(x – x') is G(x, x') (1– x')x, xх d(x – x') G(x, x') X x' 1 Use G to determine the displacement y(x) for the uniform force f = 1. Note: Be very careful with the use of G for x' < x and x' > x. Next, check that your result satisfies the differential equation and the boundary conditions. If it does not, correct your mistake or mistakes!
5. For a string under tension, small displacements y(x) due to a static force f(x) satisfy -y"(x) = f(x). For fixed boundary conditions y(x = 0) = 0 and y(x = 1) = 0, the Green's function for a delta function force 8(x – x') is G(x, x') (1– x')x, xх d(x – x') G(x, x') X x' 1 Use G to determine the displacement y(x) for the uniform force f = 1. Note: Be very careful with the use of G for x' < x and x' > x. Next, check that your result satisfies the differential equation and the boundary conditions. If it does not, correct your mistake or mistakes!
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Transcribed Image Text:5. For a string under tension, small displacements y(x) due to a static force f(x) satisfy
-y"(x) = f(x). For fixed boundary conditions y(x = 0) = 0 and y(x = 1) = 0, the Green's
function for a delta function force 8(x – x') is
G(x, x')
|(1-x )x, x<x
8(x – x')
G(x, x')
x (1-х), х>х
x'
1
Use G to determine the displacement y(x) for the uniform force f = 1. Note: Be very
careful with the use of G for x' < x and x' > x. Next, check that your result satisfies the
differential equation and the boundary conditions. If it does not, correct your mistake or
mistakes!
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