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| Category | Assignment | Subject | Engineering |
|---|---|---|---|
| University | _ | Module Title | Unit 4002 Engineering Mathematics |
| Programme Title | Higher National Certificate in Mechanical/Manufacturing/Electrical and Electronic/Embedded Electronic Engineering |
| Student Name/ID Number | |
| Unit Number and Title | Unit 4002 Engineering Mathematics (A/651/0708) |
| Academic Year | 2025-2026 |
| Unit Tutor | S. Sukomal |
| Assignment Title | 1: Use analytical and computational methods for solving problems by relating sinusoidal wave and vector functions to their respective engineering application |
| Issue Date | 04/11/2025 |
| Submission Date | 01/12/2025 |
Your assignment should be in the form of a professionally presented report with all sources used acknowledged using Harvard referencing. This assignment should be typed in full, and all calculations must be shown in order to demonstrate your understanding of the tasks. You should keep a copy of your assignment for your own records.
This assignment is to be submitted directly to your tutor by the date shown on the front of this assignment brief. Formative feedback will be provided if your report is handed to your tutor no later than 24/11/2025.
LO3 Use analytical and computational methods for solving problems by relating sinusoidal wave and vector functions to their respective engineering applications
Transferable skills and competencies developed
You work as a calibration engineer for a company that manufactures avionic measurement and control equipment for the aerospace industry. As part of a larger project, your manager has asked you to analyse a number of devices to ensure they are calibrated and operating correctly and are fit for purpose.
| Student Number | A | B | C | D | E |
| 2 | 220 | 120 | 4 | 6 | 9 |
You are testing an electronic circuit, and you discover that there are two voltage sources in separate parts of the circuit. The voltages can be modelled by the following equations:
V1= A sin ( 100 + /9 )
V2= B sin ( 100t2/5 )
i) To investigate these voltages, you are required to determine the following parameters: amplitude, phase angle and frequency, and the periodic time of each of these waves.
ii) The power sources are switched on simultaneously. How many seconds does it take for each respective voltage to reach its maximum?
iii) You believe that there is a link that is combining the voltages V1and V2. As a result, you would like to determine the nature of this combined waveform. Use appropriate compound angle formulae to expand the expressions for both V1 and V2into the form:
V_a = M sin〖100t & N cos100t 〗
where M and N are real numbers and Va= V1or V2. You should determine the values of M and N for both expressions.
iv) Using your solution from (iii), express the resultant of V1+ V2in the form:
V_res = R sin(100t)
where R = amplitude of the resultant and = phase angle
v) Your manager would like a graphical illustration of the addition of the voltages and has asked you to use appropriate software to plot V1and V2. With the aid of the software, plot the resultant of V1+ V2over two cycles to confirm the analytical solution by finding the amplitude and phase angle.
The top of a support post in the workshop is acted on by three forces: F1, F2 and F3
F1 has a magnitudeCand acts in the direction (1, 2, 2)
F2 has a magnitude 3 and acts in the direction (1, 2, -2)
F3 has a magnitude 4 and acts in the direction (3, -2, 3)
Your manager is concerned about the stability of the support and has asked you to investigate. Determine the resultant force acting on the top of the support. Confirm your analytical result using suitable existing formulae in mathematical software such as Excel.
A force has components in the x and y directions respectively of 2 N andDN. Express this in unit vector form (i.e. ai + bj). The force acts on an object which moves from (1,5) to (6,E). Express the displacement in the formci + dj and hence determine the work done using the dot product (Note: Work done = Force*Displacement). The unit of displacement is 1 metre. Confirm your analytical result by using a suitable existing formula in mathematical software such as Excel.
Please note that the resources listed are examples for you to use as a starting point in your research the list is not definitive.
Course notes for Engineering Mathematics LO3 on UCN VLE
Bird J. (2021)Higher Engineering Mathematics. 9thEd. Routledge
Stroud, K.A. and Booth, D.J. (2020)Engineering Mathematics8thEd. Bloomsbury Publishing
| Pass | Merit | Distinction |
| LO3Use analytical and computational methods for solving problems by relating sinusoidal wave and vector functions to their respective engineering application. | D2 Apply engineering mathematical software to confirm the analytical solutions for at least three engineering/manufacturing problems involving sinusoidal and vector functions. | |
| P6 Solve engineering/manufacturing problems relating to sinusoidal functions.
P7Use appropriate methodology to determine engineering parameters of data represented in vector form. |
M3Use compound angle identities to combine individual sine waves into a single wave and illustrate graphically. | |
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