EG-264 CAE MATLAB Assignment 2021/2022 Page 1 of 3 PTO EG-264 – C1 - MATLAB Coursework (50%) 2021/22 Turnitin Submission Deadline: 4pm Thursday 4th November 2021 Basic details You are asked to submit your MATLAB solution to the problems specified below. For this INDIVIDUAL assignment, a professional presentation of your solution is required. The single PDF document submission should contain the combined contents of: 1. A cover page giving your name and your student number and including the signed statement "I confirm that I have not received help from, or given help to, anyone else in constructing the solution to this individual assignment, and I certify that this is all my own work ". (See Cover Page Template, after Questions). 2. A brief description of the question and the process you have followed to produce your solution. 3. Your full MATLAB code in PDF format (use Print to PDF. i.e. NOT retyped by you and NO screenshots). 4. Your actual outputs from MATLAB in PDF format giving the answers requested (i.e. Command window outputs and figures (NOT retyped by you and NO screenshots)). 5. Appropriate referencing to any publication or web-based material that you have used in constructing your solution. N.B - NO MATLAB in-built functions on numerical integration and Bisection Method, are permitted in the construction of submitted code. The report should be saved as a single PDF document and submitted through Turnitin via Canvas. Your name and student number must be clearly visible. In addition to your PDF report, you must submit your working MATLAB files to the Canvas submission link to verify functionality of the code (there should be two .m files, one for each of the two questions in the coursework). Marking Overall, for this piece of coursework, marks will be awarded as follows: 1. The quality of the submitted report: 20% 2. The accuracy of the results: 50% 3. The MATLAB techniques used to obtain the solutions, the ease of understanding of the output (eg. comments describing code) and the quality of the documentation within the MATLAB files: 30% NB – A report should be less than 15 pages, but the MAXIMUM page limit is 18 Pages for the entire PDF submission. Any pages after this limit will NOT be marked! Submission details Coursework submissions must be submitted to Canvas BEFORE 4pm on Thursday 4th November 2021 Work that is submitted late (AFTER 4pm 4th November 2021) will be awarded ZERO marks. Late submission due to certificated illness will be dealt with according to standard procedures. EG-264 CAE MATLAB Assignment 2021/2022 Page 2 of 3 PTO Question 1: Figure 1 shows a simplified speed (mph) against time (s) graph of an off-road bicycle over a 30 second period. During the 30 seconds, the cyclist drops down a steep incline, followed by pedalling up a more prolonged incline. Figure 1: Off-road cycling Speed (mph) vs. Time(s) graph. Equation (1) reproduces the speed from time inputs as in figure 1. () = ( + ) (−./) (Eqn. 1) To determine the distance travelled by the bicycle in this timeframe, numerical integration can be used on the reproduced speed vs. time data, to calculate the area under the curve. Any of the three methods of numerical integration taught during the module (Composite Mid-Point, Trapezoidal or Simpsons Rule) can be used to determine the distance travelled by the bicycle represented in Figure 1 and Equation 1. Clearly state whichever method you are using, but you must obtain an approximation of the distance travelled by the vehicle in SI units, with a relative error of less than 0.00002%, when the analytical value is NOT known. During the numerical integration calculations, if the relative error is not reached during a loop, double the number of separations used over the timespan in the calculations for the following calculation cycle. (i) In the command window, display the integral value calculated for distance, the number of sections used in the numerical integration, and the relative error produced for each looped calculation using ‘fprintf’ and associated commands. (ii) Produce a single figure with two subplots, (1) showing the speed (m/s) vs. time (t) of the speed equation in one plot at a reasonable accuracy, and (2) a cumulative distance (m) graph of the vehicle over time (s) in the second subplot. (iii) Produce a figure showing the total distance calculated against the number of separations used in each numerical integration calculation; use a logarithmic x-axis scale on the resulting plot. [25 Marks] EG-264 CAE MATLAB Assignment 2021/2022 Page 3 of 3 PTO Question 2: For an overdamped system, the displacement of that system over time (x(t)) can be calculated using Equation (2), while incorporating equations (3) and (4) for the parameters a1 and a2 respectively and equations (5) and (6) for 1 and 2 respectively. The initial condition of v0 (initial velocity) is unknown. The initial velocity (v0) can be determined by using the parameters detailed in Table 1 and by using the Bisection method. () = − (1 −(√2−1) + 2 (√2−1)) (Eqn. 2) 1 = −0+(−+√2−1)0 2 √2−1 (Eqn. 3) 2 = 0+(+√2−1)0 2 √2−1 (Eqn. 4) 1 = − − √2 − 1 (Eqn. 5) 2 = − + √2 − 1 (Eqn. 6) Table 1: Parameter definitions, values, and units of measure Definition Parameter Value Units Stiffness 1.584 N/m Mass 1.692 kg Damping coefficient c 8.84 Kg/s Initial Displacement 0 0.2458874 m Initial Velocity 0 Unknown m/s Time 6.838 s Displacement 0.37328 m Natural Frequency = √/ Rad/s Critical Damping Ratio = 2√ ∗ Kg/s Damping Ratio = / - With the initial velocity (0) unknown: (i) Use the bisection method to determine an approximation of the value of 0, with an absolute error of less than 1 × 10−6 ; when the displacement x = 0.37328m, at time t = 6.838s, limiting the useable values of 0 between: 4 < 0 < 5.5. Display the iteration cycle number, the resulting value of 0 for each calculation cycle, and the absolute error obtained. (ii) Produce a plot of the displacement x(t), between 0 < < 15, using the initial velocity 0 calculated in part (i) and clearly highlight the values of x and t stated in table 1 on the figure of x(t). [25 MARKS] College of Engineering Coursework Submission Sheet By submitting this coursework: I confirm that I have not received help from, or given help to, anyone else in constructing the solution to this individual assignment, and I certify that this is all my own work. Submission date ……………………………………… Student signature ………………………………………………… SPLD Students Please tick this box if you are officially recognised by the University as an SPLD student. Coursework Title: ………………………………… Coursework number (i.e. CW1 CW2)………….. Module code: ………………………………… Module title: …………………………………… Submission deadline: .......……………………. Lecturer: ………………………………………………. Student number: ……………………………… Name: .........................................................………. 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