© 2021 UniCourse Ltd. All Rights Reserved Page 1 of 5 Higher National Assessment Designed in accordance with HEA guidelines Note: Assignments will not be accepted for assessment without your Email Address confirming authenticity. Learner Name: Year of Course 1 Programme Title Pearson BTEC Level 4/5 Higher National Certificate/Diploma in Engineering (RQF) Programme No BBYH8 - BBYH9 - BBYJ1 DBMT1 – DBMT4 Unit Title 2. Engineering Maths (L4) Unit Code M/615/1476 Assignment Title Analytical & Computational Methods Assignment No 2 of 3 Author Jamie Caulfield Assessor Engineering Team Internal Verifier Michael Lopez Verification Date 2nd April 2021 Week of Issue Due Week Date Submitted Agreed Resubmission Date Date Resubmitted 21 24 Please append your answers to the end of this brief. Include ALL pages of this brief in your submission. Do not submit separate documents unless requested. PLEASE NOTE: Provide a Table of Contents for your answers, indicating the page number for each of these. Please also provide inline references for your sources of information and a REFERENCES section at the end of the work, where appropriate, using the Harvard Referencing System. Assessor feedback to Learner: - Formative/Summative Grade Learner feedback to Assessor - Please tell us your thoughts about this assignment here: - I certify that the evidence submitted for this assignment is my own. I have clearly referenced any sources used in the work. I understand that false declaration is a form of malpractice. Learner Email Address: Date: I certify that the evidence submitted for this assignment is the learner’s own. The learner has clearly referenced any sources used in the work. I understand that false declaration is a form of malpractice. Assessor Signature: Date: Note: All the above information should feature on the cover page. © 2021 UniCourse Ltd. All Rights Reserved Page 2 of 5 Submission Format You should submit: - A series of hand-written and/or word-processed responses for all the given tasks. Relevant Learning Outcomes and Assessment Criteria Pass Merit Distinction LO3: Use analytical and computational methods for solving problems by relating sinusoidal wave and vector functions to their respective engineering application D2 Model the combination of sine waves graphically and analyse the variation in results between graphical and analytical methods. P6 Solve engineering problems relating to sinusoidal functions. M3 Use compound angle identities to separate waves into distinct component waves. P7 Represent engineering quantities in vector form, and use appropr ...

1. © 2021 UniCourse Ltd. All Rights Reserved
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Higher National Assessment
Designed in accordance with HEA guidelines
Note: Assignments will not be accepted for assessment without
your Email Address confirming authenticity.
Learner Name: Year of Course 1
Programme Title Pearson BTEC Level 4/5 Higher National
Certificate/Diploma in Engineering (RQF)
Programme No BBYH8 - BBYH9 - BBYJ1
DBMT1 – DBMT4
Unit Title 2. Engineering Maths (L4) Unit Code M/615/1476
Assignment Title Analytical & Computational Methods
Assignment No 2 of 3
Author Jamie Caulfield Assessor Engineering Team
Internal Verifier Michael Lopez Verification Date 2nd April
2021
Week of Issue Due Week Date Submitted Agreed Resubmission

2. Date Date Resubmitted
21 24
Please append your answers to the end of this brief. Include
ALL pages of this brief in your submission. Do not submit
separate documents unless requested.
PLEASE NOTE: Provide a Table of Contents for your answers,
indicating the page number for each of these. Please also
provide inline
references for your sources of information and a REFERENCES
section at the end of the work, where appropriate, using the
Harvard
Referencing System.
Assessor feedback to Learner: - Formative/Summative
Grade

3. Learner feedback to Assessor - Please tell us your thoughts
about this assignment here: -
I certify that the evidence submitted for this assignment is my
own. I have clearly referenced any sources used in the
work. I understand that false declaration is a form of
malpractice.
Learner Email Address:
Date:
I certify that the evidence submitted for this assignment is the
learner’s own. The learner has clearly referenced any sources
used
in the work. I understand that false declaration is a form of
malpractice.
Assessor Signature:
Date:
Note: All the above information should feature on the cover
page.

4. © 2021 UniCourse Ltd. All Rights Reserved
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Submission Format
You should submit: -
A series of hand-written and/or word-processed responses for
all the given tasks.
Relevant Learning Outcomes and Assessment Criteria
Pass Merit Distinction
LO3: Use analytical and computational methods for solving
problems by
relating sinusoidal wave and vector functions to their respective
engineering
application
D2 Model the combination of sine
waves graphically and analyse the
variation in results between graphical
and analytical methods.
P6 Solve engineering problems
relating to sinusoidal functions.
M3 Use compound angle identities to

5. separate waves into distinct
component waves.
P7 Represent engineering quantities
in vector form, and use appropriate
methodology to determine
engineering parameters.
© 2021 UniCourse Ltd. All Rights Reserved
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Unit Learning Outcomes
LO3: Use analytical and computational methods for solving
problems by relating sinusoidal wave and
vector functions to their respective engineering application.
Assignment Brief and Guidance
Scenario:
You work as a technical analyst for a large publisher of
engineering text books. One of their well-
known authors has set a number of further problems in her latest
draft engineering text, aimed at
the level four engineering market. She wishes to set these
further problems throughout the text
and intends to provide the worked solutions on a companion
website for the new book. The
author has asked you to provide these worked solutions. The

6. further problems are given in the
following tasks: -
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 may be described by…
is = 13 cos �2πft −
π
4
� [A]
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∠ �

7. 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, ��, flows through this RL
combination, causing a voltage (����) of 30V to be
developed across the resistor, and a voltage (����)
of 40V to be developed across the inductor.
Assuming that ���� is in-phase with ��, and ���� leads
���� by 90��, 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:
�� = 2�� + 3�� − 4��

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and the magnetic field as:
�� = 3�� − 2�� + 6��
Find the Cross Product of these two vectors to ascertain the
characteristics of the force on the
filament (i.e. find �� × ��).
Sketch this Cross Product (or use software to do so).
Task 3:
PART 1
The two signals below are sensed by a signal processor;
��1 = 40 sin(4��)
��2 = �� cos(4��)

9. The signal processor adds the signals to form a third signal,
which must be described as a distinct signal
in the following form;
���� = 50 sin(4�� + ��)
Use a compound angle identity to determine the value of A (the
amplitude of ��2).
Ensure that you have your calculator in Radians (RAD) mode
when determining your answer.
Use graphical software to plot/model the inputs and output of
the signal processor. How do you think
graphical methods of sine wave combination compare with
analytical methods?
PART 2
The third harmonic of a sound wave is given by;
4 cos(3��) − 6 sin(3��)
Express this sound wave in the form;
�� sin(3�� + ��)
https://www.padowan.dk/download/

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ANSWERS...
Higher National AssessmentDesigned in accordance with HEA
guidelines