MT2.solutions - ME 2fl1fi Section A Fall Semester 2Dfl3...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ME 2fl1fi Section A _ Fall Semester 2Dfl3 ngla lgfs’! @fi" Computing Techniques s-u-a Tech mung] Midterm Exam 2 Wednesday, October 22, 2W3, 4:95PM Name and entail address Stilll'l'lflhf KEY READ THIS FI HST This examination is closed hook and notes. No calculators are permitted. Use at" one sheet of formulae t3.5'*x11“} is permitted. :‘tll worlt that is submitted on this examination must be your own. Cheating will not be tolerated. and will result in immediate and strict action. Please feel free to use any pictures. _||.;:ra1:il'II.-'.1 flow charts. code iragments. or written comments in deserihing your understanding of the problem and its solution. Be sttre to clearly state art},r assumptions or conditions regarding the solution. You have approximately it] minutes for this examination {the entire class period}. A total of Hill points are awarded. The grader will lie evaluating proper organization. syntax. and punctuation. 1Write all your answers on these sheets. If necessary. use the hack—side. l-loiior Code Statement: My signature below indicates that l have read the above text. I agree to abide hy the Georgia rl'eclt Honor ltfi‘ode. I have completed this examination without external assistance. 1 have not copied any work from anotlter student during this examination. I Will not discuss this exam with another student taking this exam in this class or any other section of this class until after all exams ha in; been given. Signature: ' Question I Maximum Score Studeutls Score 1 — Short question 1 — Short question 2 - Short question 3 — Short question 4 Ln '2 :C—urve fitting: 'I'asltl Curve lining: Task 1 — Curve fitting: Task 3 3 — lsLl lieeomposition 4 — Interpolation Mat‘lah '— 21] = till} . TOTAL Page I Question 1: Short Questions {20 points; 5 points each} 1] In a lab experiment you 1verified I-lenke’s law he measuring the elongation ot‘a steel string under different tension loads. You notl.r want to determine the elongation of the string For a tension value in bemeen the load 1sadness For which you performed experiments. Should you use onn-‘e fitting or interpolation to determine this elongation?1 Explain. tlne should use curt-e fitting. Curve fitting is best used when the Functional ielationship between the variables is known {elongation = constant ’*‘ bent-lien} and the data is nois}r tss in lab experimentst. Curve Fitting will then determine the parameter 1.i'nlnes that niinimixe the deviations due to noise. interpolation. on the other hand, determines :1 I'uiietinnul relationship that passes exactly through all the points. For a noisy data set this may result in it very.- jagged eun-‘e. 3} Esninate the correlation eoef‘f'ieient For the Following data? Explain. 3.3.: . . . . . I 1 I I t The eori'eiiition eoetfieient is olose to Zero. 2g: 1' . r7 2 {st — snisi _ . '- I i i - - 'I - I ‘ - . q.- - ' ln this ease. hr is nearl e no] to 5.11 so that _ i. r a ‘10- _ : -J. 1 " ‘ - ris elose to zero. " J..'1"':-'u' ” ‘ _..‘ I ln minis: The eoi'reiation. eoelheient 3’1 E“ * . ..- .'.'-'..‘.":"':'-'" . indicates the extent to which the points .' :13 2.”: ‘ .._ '_ {91.1.1 he on a straight line. In this east. -11} .' " {Ea-,9: _ ' .1 there is no linear trend at all. or acorn ‘ .l' .- '- ' eon'eletion. I . . . -2D.' I ‘ I—.___ _ ‘33 —3D —2{} ‘10 U 10' 213 313 x Page 2 Question 2: Curve Fitting {4U paints) Seenariu: Using a GPS reeeiven you have recorded semi-:11 coordinates of a lung straight mad; 2.1.}. = 43 2:; =4m 2 y; = 3?690923 Ea. =15FJD ny =151143- zxfiyl. = ?3234 2.1}.va = 7213 fo = 4003 Zrny = 158901 2 The GPS receiver has an errtit‘ variance tirappmximately 2 meters in bath the x and y diIectiuns. it is your task In determine the most likely location of the road by fitting a straight line through the data paints. Task I {It} paints]: vaide a graphical interpretatian rat” the prahlem. Indicate clearly the mute that you plan to minimize. Justify your ehuiee. 3mg, Hat Wat fwd: [ghlei'h error: ml. 50% XML; , aflmci +9“ firm” We a? 61% file} Lt ha 390 He [5 bcei- Janeen. here {1519; fifmr firfeha‘ufi/«J‘AF i370 the JEXL'LL. Task 2 {21} points}: Devoiop tho mathematical equations for fitting a straight line through mafia (my) ooor'dinates. {Ugo a loam-Squares fonnulation} ‘11 Page 5 US-ISHW’ '- 6‘?0 7:118" __________________—_____— 4c?! . :SHHLE ~("L2J5QL Task 3 [11} points}: salve the: equations frum'task 2 and interpret the “guudness” {lme fit. | | | : 0.!755 b: Hm .gqa _79_r3 #5 £50 1 JS'HVK {7:24:91 :- —- 0.0036155 Page: 5 Question 3: Lil-Decomposition {in points) 1 5 2 Compute the Inverse ufthe folluwmg mau'ix using LET—Decarrgamfrfon: [I l 7] . fl Clearly ShDW 1mm work. 5‘ 1 xszsflf/sz Ux1b=4 a??? Klni -1h5f5‘DIq #-'-f x _ ] a2$5"5*q:_025_ Lb:g:[1}:d7 AL;[__|#D:1 a *5/51 d5: 0—Oiov—3flgl= LDJBZE Sir-7’ Alia-‘I‘EUJG f (512,]: l -* Ciro — Bimini) = FIG ng-J-jtlz. L} le: __ 1”: U x2."_11—f.(O-5'§:¥):5‘ XLr O‘D?.#L}—S¢:S“:—-53 *i'é' 24; #55 fl? 4 If *‘1‘ S A :.. 5 £3 9; Question 4: Linear Interpolation {2U points] Writc a Matlah function for I—iiirnensional linear interpolation. There should be three inputs to the function: I a 1rector with elements .‘t'.: I a vector with elements Ir; I a scalarx From 1hch Inputs. your function should compute the output, y, as shown in 111:: figure to the right. You may assume that the values of ,r.- are monotonically increasing. Cleariy state any additional assumptions you make. in the implementation of your function, you are not allowed to use The Matlah provided library i'Loietions for interpolation. function y : intl (iii, fi, 1:} 9's check whether the inputs are valid if length {xiv-=1 errorf'x meet be a sealar'}; enct if anylsize {xii ~=eize tfiii errori'xi and fi must have the same size'}: and if xitliex | xilenc‘tlex errori'extrapolation is not allowed'}; and 5’s also assume that xi are monotioally increasing a first find the two table entriee that bracket the input x n = lengthlxili for i=E:n if xiiiibx break; and and 5t: apply the intemolation formula to the entries. for iul and i y = fiti—ll + tfiti} — eiti-liiz‘ixitii-xiti—iii * ix - xiii-iii: Pagc 3 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern