4CCE1CM2 Part 2 Coursework
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4CCE1CM2
Part 2 Coursework
Coursework II
The coursework is released on 28th February 2022 and is due at 4pm on 14th March. Extensions can only be approved by applying via student records. Only students with an approved MCF should use the late submission portal. Work submitted up to 24 hours late without an approved MCF will be subject to a 10-mark deduction.
The coursework is designed to help you demonstrate that you can:
- Derive and manipulate the Laplace transforms of function, equations and systems
- Generate the step, impulse and frequency response of 1st and 2nd order systems
You should generate a PDF report containing your worked solutions, extracts of code and images of any plots you generate. The PDF should be maximum 10 pages including figures. All plots should have a title, labelled axis and units.
You may choose to use matlab livescript to produce your work and to save this as a PDF. You can input screenshots from your Simulink model into this and can generate equations. For more information about live-scripts see the guidance here.
This coursework is worth 15% of your total mark and should take around 9 hours to complete.
Figure 1 mass-spring-damper system with mass 
= 1, spring-stiffness 
= 10 and damping coefficient 
= 5. 
(
)
represents the displacement of the mass due to the input 
(
).
The mathematical model of this system is given by :
!! (
) = 
(
) − 
(
) − 
′(
)
The work below is based on the system shown in Figure 1.
Part A - Analytical (60 marks)
1. Derive the transfer function between the input force 
(
) and the position of the mass 
(
) assuming zero initial conditions [10 marks]
2. Use the Laplace Method to solve this equation for an input force 
(
) = 3
assuming zero initial conditions. [5 marks]
Plot 
(
) over time and comment on the graph. [5 marks]
3. Use the Laplace Method to solve this equation for an input force 
(
) = 3 
at 4 seconds assuming zero initial conditions. [5 marks]
Plot 
(
) over time and comment on the graph. [5 marks]
4. Derive and plot the response of the system to a unit step input using analytical methods. Use initial and final value theorems to verify your result. [10 marks]
5. Derive and plot the response of the system to an impulse input using analytical methods. Use initial and final value theorems to verify your result. [10 marks]
6. Derive the response of the system to a sinusoidal input 
2
using the Laplace method. [10 marks]
Part B – Simulink and Matlab (40 marks)
1. Investigate the lsim command in Matlab and hence verify your previous analytical answers. Hint, look at previous lecture live-scripts [20 marks]
2. Generate a Simulink model to represent this system in time (i.e. NOT using a transfer function block) and use to verify your previous answers. Hint, there is no cosine source block so consider how you might generate a cosine signal. [20 marks]
2022-03-14