1 Preamble The aim of this coursework is to enhance your understanding of the dynamics of multi-degree of freedom systems to compliment what you have learnt in the EG5027 Dynamics and

Control module. 2 Assignment Tasks (1) Derive the mass and stiffness matrices for the vibrating system shown in Figure 1. (2) Show that the natural frequencies and mode shapes of the coupled system are: f₁ = 1.24 Hz, f₂ = 2.59 Hz -0.89 = { 056 )}. {21 = {-000} {y} = 150 N m-1 www 80 Nm-1 2 kg (3) Write a Matlab program to compute the natural frequencies and mode shapes of the coupled system and compare the results obtained with the values given in Part (2). [20%] U/1 140 Nm wwww 1 kg Figure 1: A 2DOF vibrating system. [10%] U₂ [40%] [30%]/n3 Assignment Submission Format You are required to a PDF file of no more than four A4 pages showing: (a) The derivation of the mass and stiffness matrices of the system. (b) The derivation of the natural frequencies and mode shapes of the system. (c) The listing of your Matlab® script for calculating the natural frequencies and mode shapes of the system (Note: you should list the code within the PDF file as plain text, you are not required to submit your M-file.) (d) Comment(s) on the results obtained in (b) and (c). The page layout should be portrait, single column and margins should not be less than 20 mm. The file should be typeset with a minimum font size and linespacing of 12pt and 1.5, respectively. Equations prepared using technical typesetting software, such as LATEX or Math Type, are preferred, but if you are not able to do so, high-quality scanned clear and legible hand-prepared equations are acceptable. No title page is required for the PDF file. Pages of the file should be numbered consecutively and shown on the centre footer of each page. Your student number must be clearly shown on the right header of all pages. The PDF file should have the module code, your student number, assignment identifier as the filename; and 'pdf' as the extension, in the form of EG5027_u1234567_CW1R.pdf.¹