Differential Equations and MatricesThis is an individual coursework.Percentage of module mark: 30Intended Learning Outcomes:1.Ability to formulate and analyse mathematical models of engineering problems2.Ability to apply mathematical techniques and modernmathematical software tosolving engineering problems, in particular: solution of ordinary differential equationsusing analytical techniques and MatlabHand Out: 28th October 2013Hand in: 10th January 2014Question 1: 30 marksQuestion 2: 35 marksQuestion 3: 35 marksTotal: 100 marksAll students have been assigned a unique numberNwhich is used for setting parametervalues in all questions.Please look up your number in the table provided with this assignment!REMEMBER: coursework hand-in now has a hard deadline. Be late, get zero(ABsent / failure to submit). Plan to hand in at least a day early. Better still, a week.For full marks, all working must be shown.Where boxes are provided, please fit all the working and the answers in the boxes.You are allowed to use Matlab unless specified otherwise explicitly. You are not allowed touse software not covered in the module (e.g. Mapleor Simulink)Please submit an electronic version via Moodle. Only two files up to 20 Mb can be uploadedto Moodle, multiple files can be combined in a ZIParchive if necessary. It is howeverrecommended to only submit one file.208MAE, coursework 1 (2013/2014)Page 2 of 201 Beam bendingProblem:A uniformly thick beam of lengthLwith square cross-section with widthahas a distributedforce,??????+=xeLxQxq22sin1)(pN/m,applied0=xtoLx=(Qis a constant). A point forcePis applied atLx=.Pxyx= 0qx L=Find expressions for shear and momentanalytically(not using Matlab).Sketch distributions of shear forces and moment along the beam length (using Matlab)Parameters:Values ofL, EI, QandPfor each student are calculated as follows (hereNis the numberassigned to you in the table):NL*01.01+=(m)600/)300(*50NP=(kN)300/5NeQ=(kN/m)5106?=EI(Pa m4)Marking scheme:Finding correct expressions for shear and momentANALYTICALLY(not using Matlab,please show your working)(20 marks)Plots of shear force and moment(10 marks)208MAE, coursework 1 (2013/2014)Page 3 of 20Solution:1. Correct parameters for my student numberN=L=P=Q=EI=2. ShearEquation for shear:General solution of shear equation (please put yourworking here):
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