Engineering maths struggle

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Higher National Certificate/Diploma Assessment

Qualification Pearson BTEC Higher Nationals for England (2024)

Unit number and title 4002. Engineering Mathematics

Assignment title Analytical & Computational Methods

Assessor Engineering Team

Academic year 1 Unit Code A/651/0708 Assignment 2 of 3

Internal Verifier Mike Shaw Verification Date 2nd September 2024

Issue Date 2nd September 2024 Final Submission Date No later than 31st August 2025

Submission Format All text elements of your submission should be word processed, mathematical solutions can be handwritten (neatly) and scanned into your document. Assignment Format

• Organisation: Use clear headings, paragraphs, and sub-sections, to ensure clarity and ease of reading. • Referencing: Support your work with research. Use Harvard referencing or an approved alternative. Ensure accuracy to

avoid plagiarism. • Bibliography: Include a bibliography listing all referenced sources at the end, following the same referencing style.

Assignment Structure

Your assignment MUST include the following sections:

• Cover Page: Your Course, Name, Unit Name and Assignment number/name • Contents Page: List tasks or questions with page numbers. • References: List all sources used, but do not use Wikipedia.

Submission Requirements

By submitting your assignment, you confirm the following:

• Originality: The work is your own, with all sources properly cited. • Plagiarism: You acknowledge that plagiarism and collusion are forms of academic misconduct and are strictly prohibited. • Plagiarism Detection: Your assignment will be submitted to TurnItIn, a plagiarism detection service, that compares your

work against databases, online sources, and other students' work. • False Declaration: Making a false declaration is academic misconduct.

Professional Conversation

• Selected assignments will require a video conference to assess understanding before final grades are issued.

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Vocational Scenario or

Context

You work as a Test Engineer for a global manufacturer of electrical and mechanical

components and systems. Your Line Manager is responsible for delegating to you and your

colleagues the testing of theory, principles, and hypotheses from several worldwide

company divisions. She has asked you to undertake a series of such evaluations.

Task 1

Note: You need to have your calculator in radians (RAD) mode for this task (since the angles are given in radians - i.e., π is featured).

a) A current waveform in a robotic arm may be described by…

is = 13 cos �2πft − π 4 � [𝐴𝐴]

where frequency, f = 1Hz and t represents time.

Make time (t) the subject of this formula and hence determine a point in time when the current waveform has a magnitude of +10A.

b) The instantaneous value of a power signal may be described by;

12∠� 3π 8 � [W]

Find the magnitude of the vertical and horizontal components of this signal.

Note that the symbol ∠ indicates ‘angle’.

Task 2

a) A resistor, R, is connected in series with an inductor, L. An a.c. current, 𝑖𝑖, flows through this

RL combination, causing a voltage (𝑉𝑉𝑅𝑅) of 30V to be developed across the resistor, and a voltage (𝑉𝑉𝐿𝐿) of 40V to be developed across the inductor. Assuming that 𝑉𝑉𝑅𝑅 is in-phase with 𝑖𝑖, and 𝑉𝑉𝐿𝐿 leads 𝑉𝑉𝑅𝑅 by 90𝑜𝑜, draw a vector diagram for this arrangement and then calculate the magnitude of the resultant voltage across the whole RL combination.

b) A current-carrying filament is subjected to a strong magnetic field within an experimental

chamber. It is required to find the force on the filament. The current may be modelled in three-dimensional space as:

𝐼𝐼 = 2𝑖𝑖 + 3𝑗𝑗 − 4𝑘𝑘

and the magnetic field as: 𝐵𝐵 = 3𝑖𝑖 − 2𝑗𝑗 + 6𝑘𝑘

Find the Cross Product of these two vectors to ascertain the characteristics of the force on the filament (i.e., find 𝐼𝐼 × 𝐵𝐵). Sketch this Cross Product (or use software to do so).

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Task 3

PART 1

The two signals below are sensed by a signal processor;

𝑣𝑣1 = 40 sin(4𝑡𝑡)

𝑣𝑣2 = 𝐴𝐴 cos(4𝑡𝑡)

The signal processor adds the signals to form a third signal, which must be described as a distinct

signal in the following form;

𝑣𝑣𝑜𝑜 = 50 sin(4𝑡𝑡 + 𝛼𝛼)

Use a compound angle identity to determine the value of A (the amplitude of 𝑣𝑣2).

Ensure that you have your calculator in Radians (RAD) mode when determining your answer.

PART 2

The third harmonic of a sound wave is given by;

4 cos(3𝜃𝜃) − 6 sin(3𝜃𝜃)

Express this sound wave in the form;

𝑅𝑅 sin(3𝜃𝜃 + 𝛽𝛽)

Task 4

a) Use Graph software to plot the current signal given in Task 1 (a). Provide a screenshot of

your waveform.

b) Use Graph software to plot the two voltage signals (𝑣𝑣1 𝑎𝑎𝑎𝑎𝑎𝑎 𝑣𝑣2) given in Task 3 Part 1.

Provide a screenshot of your waveforms.

c) Use Geogebra to plot the vector given in Task 1 (b). Provide a screenshot of this vector

function.

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Sources of information to

support you with this Assignment

Bird J. (2021) Higher Engineering Mathematics. 9th Ed. Routledge. Bird J. (2019) Science and Mathematics for Engineering. 6th Ed. Routledge. Glyn J. and Dyke P. (2020) Modern Engineering Mathematics. 6th edition. Pearson. Made Easy Editorial Board (2022) Engineering Mathematics for GATE 2023 and ESE 2023 (Prelims) – Theory and Previous Year Solved Papers. India: Made Easy Publications Pvt Ltd. Rattan K.S., Klingbeil N.W., and Baudendistel C.M. (2021) Introductory Mathematics for Engineering Applications. 2nd Ed. Wiley. Ram M. (2021) Recent Advances in Mathematics for Engineering. CRC Press. Teodorescu P., Stanescu N., and Pandrea N. (2013) Numerical Analysis with Applications in Mechanics and Engineering. Wiley-IEEE Press. Ram M. (2020) Mathematics in Engineering Sciences: Novel Theories, Technologies, and Applications. 1st Edition. CRC Press. Sobot, R. (2022) Engineering Mathematics by Example. 1st Ed. Springer. Stroud, K.A. and Booth, D.J. (2020) Engineering Mathematics. 8th Ed. Bloomsbury Publishing Urbano M. (2019) Introductory Electrical Engineering with Math Explained in Accessible Language. Wiley. Vick B. (2020) Applied Engineering Mathematics. CRC Press.

Revant Learning Outcomes and Assessment Criteria

Pass Merit Distinction

L03

Use analytical and computational methods for solving engineering and manufacturing sector problems by relating sinusoidal wave and vector functions to their respective applications

P6 Solve engineering/ manufacturing problems relating to sinusoidal functions.

M3

Use compound angle identities to combine individual sine waves into a single wave, and illustrate graphically.

D2

Apply engineering mathematical software to confirm the analytical solutions for at least three engineering/ manufacturing problems involving sinusoidal and vector functions.

P7

Use appropriate methodology to determine engineering parameters of data represented in vector form.