ENGR Spring Exam 2

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1 ENGR 1300 Spring 013 Exam INSTRUCTIONS: Duration: 60 minutes Keep your eyes on your own work! Keep your work covered at all times! 1. Each student is responsible for following directions. Read carefully.. MATLAB and Excel commands are provided on the next page. 3. This exam consists of 8 questions on 7 pages (4 sheets front AND back). Check to be sure that you have all of the pages. 4. Write your name, PUID, Section #, and Team # on both sides of the answer sheet. 5. Closed book and notes. 6. No calculators. 7. Please make sure you return the answer sheet (you may keep this booklet). 8. Element-by-element computations are to use appropriate notation ONLY where necessary. Academic Integrity Statement I have not used material obtained from any other unauthorized source, either modified or unmodified. Neither have I provided access to my work to another. The solutions I am submitting are my own original work.

2 Exam Formula Sheet ENGR 1300 Spring 013 s s Statistics Equations 1 n 1 n n i1 n i1 n xi i n n 1 ( x i x) 1 xi + - * / ^ =.*./.^ % & ~ && = = < > <= >= ' (transpose), : ; [ ] (null vector) ( )... (ellipsis) abs acos all any asin atan clc clear cos csc disp doc cumsum else elseif error exit exp factorial figure MATLAB Functions / Operators find log for log10 format logspace fprintf lookfor function max grid mean help median hist min hold NaN i, j ones if pi Inf plot input prod leg quit length round linspace sec load sin size sort sqrt std subplot sum set tan title while who whos xlabel xor ylabel zeros Selection of MATLAB plot Special Characters Line Type Indicator Point Type Indicator Color Indicator solid - circle o blue b dotted : x-mark x green g dash-dot -. plus + red r dashed -- square s black k Excel Functions + - * / ^ = EXP MIN STDEV $ IF MODE SUM ABS LN OR TAN AND LOG10 PI AVERAGE MAX SIN COS MEDIAN SQRT

3 Problem #1 (5 points) What will be displayed on the Command Window when a script file including the following set of commands is executed? [Circle only one answer] Twater = 175 % water temperature in centigrade if Twater > 50 fprintf( Warm water ) elseif Twater > 100 fprintf( Hot water ) else fprintf( Cold water ) a. Warm water b. Hot water c. Cold water d. None of the above Solution: a. Warm water Problem # (5 points) Steve designed a mechanical sieve to separate sand into grain sizes that could be applied to paper to make commercially acceptable sandpaper for the European market. The sieve plates were given hole sizes to correspond to standards set by the Federation of European Producers of Abrasives (FEPA) for extra course, course, medium fine, and very fine grit paper. His rationale for the sieve plate hole sizes was: [Circle only one answer] a. Data analysis based b. External research based c. Casual personal experience based d. Theory based Solution: b. External research based 3

4 Problem #3 (5 points) A. Develop two distinct test cases to test the paths in the flowchart below. For each test case: 1. Define the inputs x and y. Guideline: select even integers greater than 0 and less than 7 for x and y.. Provide the displayed values of x, y, and z 3. State the purpose of the test case. Start Input x & y Is y larger than x? False Is y smaller than 0.5x? False True True z is y divided by x Add to y Display x,y,z z is y divided by 0.5x End Inputs Display x y x y z Purpose Test Case 1 Test Case 4

5 Solution: Need to provide of the 3 cases below. Inputs Display x y x y z Purpose Test Case A x y>x x y y/x takes true path from first decision TC_A Example: Test Case B TC_B Example: Test Case C TC_C Example: 4 4 x y<= x & y < x/ x y+ iter* y/x x y<= x & y >= x/ executes the loop x y y/x avoids the loop B. Write a user-defined function called Exam_Problem by converting the following flowchart exactly to MATLAB code. No commenting is necessary. Solution function Exam_Problem(x,y) if y > x z = y/x; else while y < 0.5*x y = y + ; z = y/(0.5*x); fprintf('x = %i, y = %i, z = %i \n',x,y,z) % fprintf('x = %d, y = %d, z = %d \n',x,y,z) % fprintf('x = %g, y = %g, z = %g \n',x,y,z) 5

6 Problem #4 (0 points) An apple falls with an acceleration due to gravity, g, of 9.8 m/sec. When a time variable, t, is defined, its downward velocity is then gt, and its downward displacement is (gt )/. A. Write a MATLAB definite loop to construct velocity and displacement vectors that contain the velocity and displacement values for every 0.1 sec of the first second of freefall. B. Perform the same task in MATLAB with vector calculations using a minimum number of lines of code. Solution: A. g = 9.8; % gravity [m/sec^] index = 0; for t = 0:0.1:1 index = index + 1; velocity(index) = g*t; displacement(index) = g*t^/; B. t = 0:0.1:1; g = 9.8; % gravity [m/sec^] velocity = g*t; displacement = g*t.^/; 6

7 Problem #5 (10 points) For each task (A-E) described below, indicate the most appropriate MATLAB approach from the list (a-c) below. a. while loop b. for loop c. MATLAB array operations and/or built-in functions A. Record data from every fourth sensor along an assembly line with sensors. B. Determine the number of terms from the Taylor series to use to estimate sin(x) to a specified level of accuracy. ( ) C. Continue to ask a user for input until a valid response is given. D. Determine whether there are values in an array that are less than 5. E. Keep the temperature in a house at or above 65 o F. Solution A. b. for loop B. a. while loop C. a. while loop D. c. vector operators E. a. while loop 7

8 Problem #6 (5 points) Convert this MATLAB while loop into an equivalent for loop with identical output. x = 15; while x>=3 fprintf('x = %i \n',x) x = x - 3; Solution: for x = 15:-3:3 fprintf('x = %i \n',x) Problem #7 (10 points) The following MATLAB code is executed. counter = 1; x = 0; for test = [1-6] counter = counter + 1; x(counter) = x(counter-1) + test + 1; After execution, what are the final value(s) of: A. counter? B. test? C. my_x? Solution A. 4 B. 6 C. [0 1 8] 8

9 Problem #8 (0 points) What output will appear in the MATLAB Command Window when the following code is executed? a = [ ; ; ; ]; fprintf( n b k\n ) n = 4; k = -1 while n > 0 b = 1; fprintf( %i, %i, %i\n,n,b,k) while b <= n b = b + ; k = a(n,b) * ; fprintf( %i, %i, %i\n,n,b,k) n = n 3; fprintf( %i, %i, %i\n,n,b,k) Solution n b k % a(4,3)* = 1* = % a(4,5)* = 0 * = % a(1,3)* = -10* =

January 18, 2008 Steve Gu. Reference: Eta Kappa Nu, UCLA Iota Gamma Chapter, Introduction to MATLAB,

January 18, 2008 Steve Gu. Reference: Eta Kappa Nu, UCLA Iota Gamma Chapter, Introduction to MATLAB, Introduction to MATLAB January 18, 2008 Steve Gu Reference: Eta Kappa Nu, UCLA Iota Gamma Chapter, Introduction to MATLAB, Part I: Basics MATLAB Environment Getting Help Variables Vectors, Matrices, and