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ASE 311 HW #10

ASE 311 HW #10 - Usman Ansari ASE 311 HW#10 1 a > u=1800...

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Usman Ansari ASE 311 HW #10 1.) a.) >> u=1800; mo=160000; q=2500; g=9.8; z(1)=-sqrt(3/5); z(2)=0; z(3)=-z(1); w(1)=5/9; w(2)=8/9; w(3)=5/9; stretchFactor = 30 / 2 ; t = 15 + 15 * z ; y = (u * log(mo./(mo - q*t)) - g*t) d = stretchFactor*(sum(w.*y)) y = 64.5617 333.7130 707.0288

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Usman Ansari ASE 311 HW #10 d = 1.0879e+004 b.) >> u=1800; mo=160000; q=2500; g=9.8; z(1) = -sqrt(245 + (14*(sqrt(70))))/21; z(2)= -sqrt(245 - (14*(sqrt(70))))/21; z(3)=0; z(4)=-z(2); z(5)=-z(1); w(1)=((322-(13*sqrt(70)))/900); w(2)=((322+(13*sqrt(70)))/900); w(3)=128/225; w(4)=w(2); w(5)=w(1); stretchFactor = 30 / 2 ; t = ( 15 + 15 * z ) ; y = (u * log(mo./(mo - q*t)) - g*t);
Usman Ansari ASE 311 HW #10 d = stretchFactor*(sum(w.*y)) d = 1.0880e+004 c.) >> u=1800; mo=160000; q=2500; g=9.8; quad(@(t)u * log(mo./(mo - q*t)) - g*t , 0 , 30) ans = 1.0880e+004 (m) 3 point gauss-legendre 10879.43 5 point gauss-legendre 10879.62 Quad 10879.62

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Usman Ansari ASE 311 HW #10 2.) >> x = 1; xi = [ .6 , 1.5 , 1.6 ] ; f = ( 5 * exp ( -2.* xi ).* xi ) ; fd = (f(1).*(2*x-xi(2)-xi(3)))./((xi(1)-xi(2)).*(xi(1)-xi(3))) + (f(2).*(2*x-xi(1)-xi(3)))./((xi(2)- xi(1)).*(xi(2)-xi(3))) + (f(3).*(2*x-xi(1)-xi(2)))./((xi(3)-xi(1)).*(xi(3)-xi(2))) fd = -0.6007
Usman Ansari ASE 311 HW #10 >> x = 1.4; xi = [ .6 , 1.5 , 1.6 ] ; f = ( 5 * exp ( -2.* xi ).* xi ) ; fd = (f(1).*(2*x-xi(2)-xi(3)))./((xi(1)-xi(2)).*(xi(1)-xi(3))) + (f(2).*(2*x-xi(1)-xi(3)))./((xi(2)- xi(1)).*(xi(2)-xi(3))) + (f(3).*(2*x-xi(1)-xi(2)))./((xi(3)-xi(1)).*(xi(3)-xi(2))) fd = -0.5079

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