# Applied Engineering Mathematics

Assignment 2

Engineering Mathematics

Applied Engineering Mathematics

55-4852 Applied Engineering Mathematics

ii)        Complete all questions ‘by hand’ unless otherwise instructed. However, if you cannot complete, for example, part b) of a particular question, but you need the answer to b) in order to complete part c) of the same question, then you should use software to obtain the answer to b). In doing so, you will achieve partial credit for part b) and will be able to attempt part c).

iv)      If a question requires you to provide a screenshot(s) of work done using software then these need to be clear with easily legible text. Failure to do this will negatively affect your grade.

v)       You are not required to provide evidence that you have checked your answers, however, you are strongly encouraged to make good use of the mathematical and software skills you have developed in this module by using them to convince yourself that every solution you commit to paper is correct in every detail.

vi)      All extension requests are dealt with by the ACES Helpdesk.

·         40 come from the ‘routine’ type (A) questions (of which there are 12)

·         20 come from the ‘trickier’ type (B) questions (of which there are 12)

·         30 come from the ‘demanding’ type (C) questions (of which there are 5)

Questions of the same type contribute equally to the total for that type.

You will receive a grade of 0, 1, 2 or 3 for each question (see diagram below). These grades will be appropriately scaled and combined to produce your overall mark.

The remaining 10 marks on this assignment are awarded for the quality of your mathematical communication e.g. use of correct notation, short comments to clarify your calculations, no superfluous = signs etc. These marks are awarded ‘pro rata‘ insofar as attempting only 3 of the 5 questions (60% of the assignment) means you cannot score more than 6 on communication. Use the feedback from your first assignment to help you with your communication.

For anything that could have been checked without much difficulty, limited credit will be given for ‘errors carried forward’ from one sub-question to another e.g. an incorrect (but check-able) solution to part d) of a particular question could attract a grade of anything up to 3. However, if part e) is incorrect because it relied upon your answer to part d), then part e) will receive a grade of no higher than 1.

to the points , , , , and .

(A)

and use an appropriate piece of software to determine the elements of . Include a clear screenshot(s) showing your inputs and the solution.

(A)

(A)

(B)

(B)

The voltages in this circuit are given by the formulae

while the current .

(A)

(A)

(A)

(B)

(B)

where, in this example, , ,  and .

(A)

(B)

(C)

produce a fully-labelled plot of the numerical and analytical solutions together on a single graph and use it to comment on whether or not the numerical solution has been able to approximate the behaviour of the analytical solution.

(C)

where  is the mass of the bob,  is the length of the pendulum arm and  is gravitational acceleration N.B.  is positive when the pendulum arm is to the right of the vertical.

Given that the moment of inertia for this system is  and that the torque is related to the angular acceleration of the pendulum arm by equation

(A)

up to and including the  term.

(A)

(B)

(A)

(A)

(B)

(C)

where  represents an input to the system that is used to control the temperature . The initial temperature of the fluid is stable at  i.e.

(A)

(B)

(B)

(A)

(B)

(B)

(B)

(C)

(C)

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