1University of WollongongFaculty of Engineering and Information SciencesENGG952 Engineering ComputingSpring Session – 2017Assignment 2Rules:1. The assignment may be completed individually or by a group up to 3 students. The groupformation is your own responsibility. Members may be from the same or different tutorialgroups.2. No collaboration between groups permitted. Any case of plagiarism will be penalized andstudents should make themselves aware of the university policies regarding plagiarism (seesubject outline under University and Faculty Policies)3. The assignment is due in week 13 (Friday 27 October by 4 pm) and submitted to Central ofEIS using then barcoded sheet (see subject outline under assignment submission). Latesubmission will incur penalty as described in the subject outline.4. If the assignment is completed by group, statement indicating the effort or contribution tothe assignment by each member and signed by all members must be included in thebeginning of the report, or all students agree that they have contributed equally to thereport –add a statement at the front of the report, signed by all members.5. The assignment must be submitted as a formal report. You need to include the analysis ofthe problem, the procedure for solution, and discussion of the results. It is NOT sufficient toonly provide the program and results. All matlab script files, function files and excel filesmust be included as attachments or main contents in the hard copy report.6. In addition, all matlab codes and function files must be burned in a CD or USB andsubmitted with the report for checking.2Question 1: Motion of a Spring-Mass System (50%)The motion of a damped spring-mass system is descirbed by the following ordinarydiffernetial equation:0 22 kx dtdxcdtd xmwhere x is displacement from equlibrium position (meter), t is time (second), m is the massand equal 20 kg, c is the damping coefficient (N.sec/meter) . The dampping coefficient, c,takes on two values of 5 (under damped), 39(critically damped. The spring constant k = 20N/meter. The initial velocity is zero, and the intial displacement x = 1 meter.Figure 1. Damped spring-mass system(a) Transform the problem into a system of two first order initial value ODEs. The reportmust clearly provide the detailed derivation of the technique.(b) Solve for motion of a spring-mass system using the 2nd order RK Huen method over thetime period0 t 5sec with a step sizet 1.0 . You can calcualte the resultsmanually or by matlab or by excel.(c) Plot the displacment verus time for two values of the damping coefficient on the samefigure, and discuss the results.Question 2: Transient Heat Conduction (50%)The non-dimensional form for the transient heat conduction in an insulated rod istuxu22xis the nondimensional length, tis the nondimensional time,uis the nondimensionaltemperature. This makes for the following boundary and initial conditions:Boundary conditions u(0,t) = 0.5 u(1,t) = 2.0Initial conditions u(x, 0) = 0.5 0 xFigure 2. Heat conduction problem in an insulated rod.Note:Lxx ,( / )2 CL ktt ,L ooT TT Tu, in which L = the rod length, k = thermalconductivity of the rod material, = density, C = specific heat, To = temperature at x = 0,and TL = temperature at x = L.Solve this nondimensional equation for the temperature distribution using explicit finite-difference method and implicit Crank-Nicholson method:a) Write the finite-difference equation of the differential equation. The report mustclearly provide the detailed derivation of the technique.b) Programing to obtain the solution for time duration0 t 1 . (For explicit finitedifference method, you can use EXCEL or matlab. For implicit Crank-Nicholsonmethod, you must use the matlab).Please demenstrate that appropriatexandtare needed to solve u until steady-state solution is reached.c) Plot the nondimensional temperature versus nondimensional length for a few typicalvalues of nondimensional times, which can demonstrate the evloution of thetempeature at different time.