HW 5 Solution - EGM3344 HW5 Solution Problem 8.3 Write the...

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Unformatted text preview: EGM3344 HW5 Solution Problem 8.3 Write the given set of equations as Ax = b (1) where A = − 7 5 4 7 − 4 3 − 7 , x = x 1 x 2 x 3 , b = 50 − 30 40 (2) Then solve for x 1 , x 2 , and x 3 : >> A = [0- 7 5;0 4 7;- 4 3- 7]; >> b = [50;- 30;40]; >> x=A \ b x =- 15.1812- 7.2464- 0.1449 Also the transpose of the coefficient matrix A T is >> A' ans =- 4- 7 4 3 5 7- 7 and the inverse of the coefficient matrix A − 1 is >> inv(A) ans =- 0.1775- 0.1232- 0.2500- 0.1014 0.0725 0.0580 0.1014 Problem 8.4 (a) The pairs which can be multiplied are: ( A , B ), ( A , C ), ( B , C ), and ( C , B ). 1 >> A = [6- 1; 12 8;- 5 4]; >> B = [4 0; 0.5 2]; >> C = [2- 2;- 3 1]; >> A * B ans = 23.5000- 2.0000 52.0000 16.0000- 18.0000 8.0000 >> A * C ans = 15- 13- 16- 22 14 >> B * C ans = 8- 8- 5 1 >> C * B ans = 7.0000- 4.0000- 11.5000 2.0000 (b) The inner dimensions of the remaining pairs ( B , A ) and ( C , A ) don’t agree, so they can’t be multiplied. (c) The order of multiplication is important since matrix multiplications do not commute (e.g., BC negationslash = CB , as seen in (a)). Problem 8.6 In matrix form, the given equations can be written as Ax = b (3) where A = cos 30 ◦ − cos 60 ◦ sin 30 ◦ sin 60 ◦ − cos 30 ◦ − 1 − 1 − sin 30 ◦ − 1 1 cos 60 ◦ − sin 60 ◦ − 1 x = F 1 F 2 F 3 H 2 V 2 V 3 b = F 1 ,h F 1 ,v F 2 ,h F 2 ,v F 3 ,h F 3 ,v (4) Use MATLAB to solve for x : prob8 6.m A = [ cosd(30)- cosd(60) 0; sind(30) sind(60) 0;- cosd(30)- 1- 1 0;- sind(30)- 1 0; 2 1 cosd(60) 0;- sind(60)- 1]; b = [0;- 1000;0;0;0;0]; x = A \ b output x =- 500.0000 433.0127- 866.0254 250.0000 750.0000 Therefore we have F 1 = − 500, F 2 = 433, F 3 = − 866, H 2 = 0, V 2 = 250, and V 3 = 750 (all in lbs). Problem 8.10 Define the displacements as shown in Fig. 1. Each mass is at rest, so the force balance equations become Figure 1: Problem 8.10 mass 1: m 1 g − kx 1 − k ( x 1 − x 2 ) = 0 (5) mass 2: m 2 g − k ( x 2 − x 1 ) − k ( x 2 − x 3 ) = 0 (6) mass 3: m 3 g − k ( x 3 − x 2 ) = 0 (7) or 2 kx 1 − kx 2 = m 1 g (8) − kx 1 + 2 kx 2 −...
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This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

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HW 5 Solution - EGM3344 HW5 Solution Problem 8.3 Write the...

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