Homework1 - 1 1 1 1 3 2 . 2 2 2 . 3 1 5 . 1 d) Solve for x...

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CEE511 – Structural Dynamics Winter Semester 2005-2006 Homework #1 (Due January 23, 2006) 1 - Trigonometry (Assume A and B are constants) a) ? ) sin( = + B A b) ? ) cos( = + B A c) Show ]) ) sin[( ] ) (sin[( 2 1 sin cos x B A x B A Bx Ax + = d) Show ]) ) cos[( ] ) (cos[( 2 1 cos cos x B A x B A Bx Ax + + = 2 - Differentiation (Assume k is a constant integer) a) () ? = kx xe dx d b) () ? cos sin = kx kx dx d c) ? sin = x kx dx d d) ? ) ln(sin ) ln(sin lim 0 = ⎯→ x x x π 3 - Integration (Assume A , B , C and k are constant integers) a) ? ) sin( = dx kx A b) ? ) sin( = dx kx x c) ? ) cos( = dx kx x d) ? )] ( sin[ ) sin( = dx x C B Ax e) ? ) cos( ) sin( = dx Bx Ax 4 - Ordinary Differential Equations (ODE) a) Solve: 0 2 2 = + + ky dx dy c dx y d m Assume c =0.5, k =0.5, m =0.5, y (0)=1, () 0 0 = dx dy
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b) Solve: x ky dx dy c dx y d m sin 2 2 = + + Assume c =0.5, k =0.5, m =0.5, y (0)=1, () 0 0 = dx dy 5 - Linear Algebra a) ? 1 0 1 3 2 . 0 2 2 2 . 0 3 1 5 . 0 1 = ⎧− b) {} ? 1 0 1 3 2 . 0 2 2 2 . 0 3 1 5 . 0 1 1 1 0 = ⎧− c) Fill in the vectors: + + =
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Unformatted text preview: 1 1 1 1 3 2 . 2 2 2 . 3 1 5 . 1 d) Solve for x , y and z: = 1 1 1 3 2 . 2 2 2 . 3 1 5 . 1 z y x 6 - Solve the following using MATLAB (Please provide your MATLAB code) Given: = 5 2 3 8 7 2 4 5 1 A = 9 2 2 4 1 B [ ] 3 3 1 = C [ ] 8 8 2 11 12 3 9 7 4 = D a) Compute the mean of D b) Compute the inverse of A and of B c) Compute the transpose of [ A + B ] d) Compute the determinate of A e) Plot ) 6 . 1 sin( 5 . 3 x for (-5 < x < +5)...
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This note was uploaded on 05/09/2008 for the course CIVIL ENGI CE 511 taught by Professor Lynch during the Spring '06 term at Michigan State University.

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Homework1 - 1 1 1 1 3 2 . 2 2 2 . 3 1 5 . 1 d) Solve for x...

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