Select Page

Your Perfect Assignment is Just a Click Away

Starting at \$8 per Page

100% Original, Plagiarism Free, Customized to Your instructions!     ## • • MAE 384 Homework #3 Page 1 of 2 MAE 384 Advanced Mathematical Methods for Engineers Homework #3 Due: Sept. 16, Tuesday in class Problem 1: Matlab Three masses are attached to spring, k1  30 N/m, 25 2 k  N/m, 20 3 k  N/m, and 15 4 k  N/m, a

·

·  MAE 384  #3 Page 1 of 2 MAE 384 Advanced Mathematical Methods for Engineers Homework #3 Due: Sept. 16, Tuesday in class Problem 1: Matlab Three masses are attached to spring, k1 = 30 N/m, 25 2 k = N/m, 20 3 k = N/m, and 15 4 k = N/m, as shown. Initially the masses are positioned such that the springs are in their natural length (not stretched or compressed); then the masses are slowly released and move downward to an equilibrium position as shown on the right. The equilibrium equations of the three masses are úúúûùêêêëé=úúúûùêêêëéúúúûùêêêëé+++ 3 2 1 3 2 1 4 4 3 3 4 4 1 2 3 3 0 0 W W W u u u k k k k k k k k k k where u1, u2, and u3 are the relative displacement (from the unstretched position) of each mass as shown. If the masses have true weights 20 1 W = N, 30 2 W = N, and 15 3 W = N. However, due to a bias error in the measuring device, the actual weight column vector on the right hand size used to determine the displacements is úúúûùêêêëé+úúúûùêêêëé=úúúûùêêêëé c c c W W W W W W 3 2 1 3 2 1 ‘ ‘ ‘ where c is a constant representing the bias error in the weight measurements. The effect of bias c on the error in the displacements u is studied by the error analysis equation [][][][][][][][][][b] r A A x e b r A A 1 1 1 ££ TS Write a Matlab script to complete the following tasks: (a) Determine the true displacements using the true weights 1 W , 2 W , and 3 W . (b) Assume the bias c changes from 0 to 5 N with a step size of 0.1 N. For each value of c, determine (1) the lower error bound [][][][b] r A A 1 1 , (2) the upper error bound [][][][b] r A A 1 , and (3) the relative error [][] TS x e . (c) Plot the lower bound vs. c, upper error bound vs. c, and relative error vs. c on the same graph (i.e., three curves in one figure). Note: Please use 1-norm for the analysis and you may use the built-in function norm for this purpose. MAE 384 Liao Homework #3 Page 2 of 2 Problem 2: By hand A dynamical system can be modeled by a system of linear equation [A][x]=[b], where [x] represents the input to the system, [b] represents the output, and the system matrix []úúúúûùêêêêëé= 3 4 2 5 2 1 1 2 1 2 3 4 5 4 3 2 A (a) Determine the condition number of the system using the infity-norm. (You may use calculators to find the inverse of the matrix.) (b) If the relative error in the output measurement is about ±2%, i.e., [r][b]= 2%, estimate the range of the relative error in the solution, i.e., [][] TS e x (c) If we want the relative error in the solution to be below 5%, what would be requirement on the relative error in the output measurement?

·

·  MAE 384 Liao Homework #3 Page 1 of 2 MAE 384 Advanced Mathematical Methods for Engineers Homework #3 Due: Sept. 16, Tuesday in class Problem 1: Matlab Three masses are attached to spring, k1 = 30 N/m, 25 2 k = N/m, 20 3 k = N/m, and 15 4 k = N/m, as shown. Initially the masses are positioned such that the springs are in their natural length (not stretched or compressed); then the masses are slowly released and move downward to an equilibrium position as shown on the right. The equilibrium equations of the three masses are úúúûùêêêëé=úúúûùêêêëéúúúûùêêêëé+++ 3 2 1 3 2 1 4 4 3 3 4 4 1 2 3 3 0 0 W W W u u u k k k k k k k k k k where u1, u2, and u3 are the relative displacement (from the unstretched position) of each mass as shown. If the masses have true weights 20 1 W = N, 30 2 W = N, and 15 3 W = N. However, due to a bias error in the measuring device, the actual weight column vector on the right hand size used to determine the displacements is úúúûùêêêëé+úúúûùêêêëé=úúúûùêêêëé c c c W W W W W W 3 2 1 3 2 1 ‘ ‘ ‘ where c is a constant representing the bias error in the weight measurements. The effect of bias c on the error in the displacements u is studied by the error analysis equation [][][][][][][][][][b] r A A x e b r A A 1 1 1 ££ TS Write a Matlab script to complete the following tasks: (a) Determine the true displacements using the true weights 1 W , 2 W , and 3 W . (b) Assume the bias c changes from 0 to 5 N with a step size of 0.1 N. For each value of c, determine (1) the lower error bound [][][][b] r A A 1 1 , (2) the upper error bound [][][][b] r A A 1 , and (3) the relative error [][] TS x e . (c) Plot the lower bound vs. c, upper error bound vs. c, and relative error vs. c on the same graph (i.e., three curves in one figure). Note: Please use 1-norm for the analysis and you may use the built-in function norm for this purpose. MAE 384 Liao Homework #3 Page 2 of 2 Problem 2: By hand A dynamical system can be modeled by a system of linear equation [A][x]=[b], where [x] represents the input to the system, [b] represents the output, and the system matrix []úúúúûùêêêêëé= 3 4 2 5 2 1 1 2 1 2 3 4 5 4 3 2 A (a) Determine the condition number of the system using the infity-norm. (You may use calculators to find the inverse of the matrix.) (b) If the relative error in the output measurement is about ±2%, i.e., [r][b]= 2%, estimate the range of the relative error in the solution, i.e., [][] TS e x (c) If we want the relative error in the solution to be below 5%, what would be requirement on the relative error in the output measurement?

"Place your order now for a similar assignment and have exceptional work written by our team of experts, guaranteeing you A results." ## Our Service Charter

1. Professional & Expert Writers: Eminence Papers only hires the best. Our writers are specially selected and recruited, after which they undergo further training to perfect their skills for specialization purposes. Moreover, our writers are holders of masters and Ph.D. degrees. They have impressive academic records, besides being native English speakers.

2. Top Quality Papers: Our customers are always guaranteed of papers that exceed their expectations. All our writers have +5 years of experience. This implies that all papers are written by individuals who are experts in their fields. In addition, the quality team reviews all the papers before sending them to the customers.

3. Plagiarism-Free Papers: All papers provided by Eminence Papers are written from scratch. Appropriate referencing and citation of key information are followed. Plagiarism checkers are used by the Quality assurance team and our editors just to double-check that there are no instances of plagiarism.

4. Timely Delivery: Time wasted is equivalent to a failed dedication and commitment. Eminence Papers is known for timely delivery of any pending customer orders. Customers are well informed of the progress of their papers to ensure they keep track of what the writer is providing before the final draft is sent for grading.

5. Affordable Prices: Our prices are fairly structured to fit in all groups. Any customer willing to place their assignments with us can do so at very affordable prices. In addition, our customers enjoy regular discounts and bonuses.

6. 24/7 Customer Support: At Eminence Papers, we have put in place a team of experts who answer to all customer inquiries promptly. The best part is the ever-availability of the team. Customers can make inquiries anytime. 