Assignment 2015 Correction
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UNIVERSITI TUNKU ABDUL RAHMAN ACADEMIC YEAR 2015-01 UEMM3243 ENGINEERING ANALYSIS ASSIGNMENT Assignment questions Su!mit in "ee# $$% &RIDAY '(M 2 stu)ents *e+ g+ou* ,$- The ends of a stretched string of length L = 1 are fixed at x=0 and x=1 The string is set to !i"rate fro# rest "$ releasing it fro# an initial triang%lar sha&e #odeled "$ th f ( x ) = { 3 10 x 0 ≤ x ≤ 1 3 3 ( 1 − x ) 20 1 3 ≤ x ≤ 1 'i!en that c = 1 π . Deter#ine the sol%tion u(x)t* +sing co#&%ter soft,are) &lot the sha&e of !i"ration for t = 0) 05) 10) 15) 20) 25) 0) on se&arate gra&h /100 ,2- +sing anal$tical #ethod) sol!e the oisson E3%ation for the follo,ing 4ig%re gi!en data) &igu+e 2 Ta e a = 2) b = 1 a* f ( x , y ) = 2 xy , f 1 ( x ) = 0, f 2 ( x ) = x ; g 1 ( y ) = sin π y , g 2 ( y ) = 2 y . "* 6ol!e (a* ,ith n%#erical #ethod and co#&are the ans,er for each node Ta i si7eh = k = 01 .- /100 1
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Transcript of Assignment 2015 Correction
UNIVERSITI TUNKU ABDUL RAHMAN
UNIVERSITI TUNKU ABDUL RAHMAN
ACADEMIC YEAR 2015-01
UEMM3243 ENGINEERING ANALYSIS ASSIGNMENT
Assignment questions. Submit in Week 11, FRIDAY 5PM .2 students per group.
Q1) The ends of a stretched string of length L = 1 are fixed at x=0 and x=1. The string is set to vibrate from rest by releasing it from an initial triangular shape modeled by the function
Given that Determine the solution u(x,t).
Using computer software, plot the shape of vibration for t = 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 on separate graph.[100%]
Q2) Using analytical method, solve the Poisson Equation for the following Figure 2 with the given data,
Figure 2Take a = 2, b = 1.a) b) Solve (a) with numerical method and compare the answer for each node. Taking the mesh size h = k = 0.1c) [100%]
Q3) For the plate shown in Figure 2, solve for Laplace Equation , provide the answer for each node of the grids which is of the size 1x1.i) using numerical methodii) using MATLAB PDETOOLS(Compare your answers for all methods size by size) [100%] Y
u = 100 5
Insulated , k = 1 h = 10, T = 25
0 u = 0 10 X
Figure 3
Notes:
1) Your member must be from the same program, i.e. CL-CL, ME-ME, CI-CI.2) Email to me your group members information, to [email protected] .
NameCourseStudent ID
1) XXXME123456
2) YYYME789236
3) You can choose to do it alone.4) Your assignments answers must be typed and printed.
References
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