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[answered] MAE 215: Introduction to Programming in MATLAB Course Proje

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MAE 215: Introduction to Programming in MATLAB


Course Project


Due: Wednesday, November 30th by midnight Submission Instructions: Your solutions to this assignment must be typed and neatly presented. Unorganized solutions and/or solutions that do not present the required


deliverables will not be graded and receive a score of zero. This assignment is to be


submitted, in PDF format, to the assignment link on blackboard by the deadline.


Students who obtain a score of 80% or greater on this project will receive credit for all course


outcomes. 1. [45 pts] Part 1 ? ?For? and ?While? loops in MATLAB




Consider the approximation for sin(x) given in homework #3 as: 3 5 7 9 11 13 15 17 = ? + ? + ?








3! 5! 7! 9! 11! 13! 15! 17!


Create a vector where each element is a term of the series. Allow the user to input the value


of x (as a scalar). Sum the terms of the series using a ?for? loop and create a formatted output


to show the user (1) the value of the approximation, (2) the actual value of sin(x) (from the


MATLAB function) and (3) the error between the two. Use values x = 2, 2.5, 3 to compare.


ii. Now consider the generalized form of the Taylor series for sin(x):


? 2+1


sin = ?(?1)


(2 + 1)! =0 Sum the first 100 terms of the series and show the result as a formatted output identical to


that of 1(i). Allow the user to input the value of x as a scalar. Repeat this problem with the


first 250 terms. Compare the results. (Use same x values as from (i)).


iii. How many terms are required in (iii) to reduce the relative error to less than 1%?




Assume that the relative error (percent) is defined as:


( ? ) % = | = sin , | ? 100 = ??


=0(?1) ( 2+1


2+1)! where St and Sn are the true and numerical solutions, respectively. The ?numerical? solution


will come from the summation of terms while the true solution can be obtained using the


built-in MATLAB function for sin(x). Each iteration through the loop, create a formatted


output that shows (1) the iteration number, (2) the number of terms in the series and (3) the MAE 215: Introduction to Programming in MATLAB


Course Project


Due: Wednesday, November 30th by midnight


percent error between the obtained values. The output printed during the loop should be


done so that a new line is created each time a new output is printed. When the loop has


completed, display the result, the final percent error, and the number of terms using a single


command. Save the percent error per iteration and plot % error vs. iteration when the loop


has completed.


iv. For (iii), create a flowchart showing the logic of your code. Considering that this is the course


project, please be sure to create this flowchart in a word editor (i.e. it must be typed!). 2. [55 pts] Part 2 ? Processing data with MATLAB




Consider the 3 text files labeled ?aluminum_test?, ?5_MIL_test? and ?2_MIL_test? that are


uploaded and attached to the assignment link. This data was collected when running


Arizona State University?s shocktube during an AEE 362 (High Speed Aerodynamics)


laboratory experiment . The tests show data for 3 different shock wave experiments where


shocks of different strengths were intentionally generated. Note that the first two columns


represent pressure data (reported in psi) and that columns 3 and 4 show pressure data in


units of Volts. Therefore, the data in columns 3 and 4 must be converted to useful units


before it can be plotted. The conversion is given below, giving you a result in PSI. = 0.0418 ? Your task is to:


a. Load this data into MATLAB (hint: load() ? you may also need to remove the text at the top of


the data file).


b. Find the total time of the dataset, noting that the time between data points is 0.025 ms.


c. Add 14.0 to all the values in the second column. Plot this data together with that of the first


column vs. time. Knowing that this is pressure, what appears to be happening?


d. Plot the data in columns 3 and 4 vs. time, after this data has been converted to PSI. These


sensors were mounted inside the tube and represent changes in pressure over time. What


can you see from the data? (quick comment)




e. The distance between the two pressure transducers is given as 4832 in. Knowing this, we can


use the ?peaks? from the data in the plot from (d) (showing two changes in pressure at two


different locations) to calculate the speed of the resulting shockwave. After generating the


plot, use the ?cursor tool? and find the between the two peaks (you may also need to zoomin considering it is the first two peaks we are interested in). The velocity of the wave can then


be calculated using: ?x


?t where is the distance between pressure sensors. Compare shock speeds between the


materials (no comments/analysis needed ? but look at the results!).


The material strengths are in the order: 5 Mil, 2Mil, Aluminum.


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