HW 5 Solution

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 −...
View Full Document

{[ snackBarMessage ]}

### Page1 / 10

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online