Unit 4002 Engineering Mathematics (A/651/0708) Assignment Brief 2025-2026, Barnsley College (BC)

Assignment Brief

Submission Format

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.

Unit Learning Outcomes

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

Vocational scenario

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.

Assignment activity and guidance

Task 1

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 ( 100πt + ^2π/9 )

V₂ = B sin ( 100πt − ^2π/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 V₁ and 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 V₂ into the form:

V_a = M sin⁡〖100πt ± N cos⁡100πt 〗

where M and N are real numbers and V_a = V₁ or V₂. You should determine the values of M and N for both expressions.

iv) Using your solution from (iii), express the resultant of V₁ + V₂ in the form:

V_res = R sin⁡(100πt ± ∝)

where R = amplitude of the resultant and α = 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 V₁ and V₂. With the aid of the software, plot the resultant of V₁ + V₂ over two cycles to confirm the analytical solution by finding the amplitude and phase angle.

Task 2

The top of a support post in the workshop is acted on by three forces: F1, F2 and F3

F1 has a magnitude C and 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.

Task 3

A force has components in the x and y directions respectively of 2 N and D N. 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 form ci + 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.

Recommended Resources

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. 9^th Ed. Routledge

Stroud, K.A. and Booth, D.J. (2020) Engineering Mathematics 8^th Ed. Bloomsbury Publishing

Learning Outcomes and Assessment Criteria

Answer

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