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School of Digital, Technology, Innovation & Business

Session: 2024/25 Semester: 1
Intermediate Engineering Mathematics
MATLAB Assignment

Assessment weighting: 25%
You are required to produce a MATLAB worksheet which answers the questions in this assignment.

Question 1: Sky Diver
Question 2: Heated Oven
As part of your answers you should include text describing, in your own words, what you have done.

Note: Practice the example problems provided before you start this assignment.

Submission
You should export your worksheet as a pdf document and should submit the exported pdf.
Additionally, you should submit the MATLAB (original script) document.

Plagiarism:
The university takes plagiarism very seriously. This is an individual piece of work and so it is essential that the final submission is your own work.

Question 1: Sky Diver

Investigate the solution to this equation using your body mass m in kg and other values as follows:

(a)Solve the equation (using dsolve function in MATLAB) and plot the solution for the range 0 < t < 20s, with your body mass along with those for m=50kg and m=100kg and comment on the result.

[10 marks]
Note: This question must be solved using MATLAB software and submit both the original script file and exported pdf with detailed explanation in your own words.

(b)Use the differential equation to find the equation for the terminal velocity. How does it relate to the mass, m and do your plots in part (a) support this?

[5 marks]
Note: You are not required to use MATLAB software to find the terminal velocity but solutions using MATLAB will be accepted.

Question 2: Heated oven

The interior temperature of a heated oven is controlled by varying the heat input to the oven jacket as shown below:

where
is the ambient temperature
is the jacket temperature and
is the oven temperature

If and if then it can be shown that

and

where and are the heat capacities of the jacket and oven and and depend on the exterior and interior surface area and radiation coefficients of the jacket.

a)Initially consider a heated oven with initial conditions with no heat input, i.e. .
(i)Using , , and .
Find the solution for any non-zero choice of .
Plot your solutions and describe and explain their behaviours.
[10 marks]

(ii) Keeping , and the same, but varying what effect is there on your solutions? You should consider cases where , and in your discussion.
[5 marks]

b) (i) Choose a value for E which is positive and using the initial conditions find the particular solution to this system of differential equations for your original values in (a) and compare it with the solution found in (a).
[5 marks]

(ii) Repeat (i) with initial conditions , using your chosen value of from (a).

[5 marks]
Note: All the above questions must be solved using MATLAB software and submit both the original script file and exported pdf with detailed explanation in your own words.

Total: 40 marks