Matlab

MAE 384 Liao Homework #2 Page 1 of 1

MAE 384 Advanced Mathematical Methods for Engineers Homework #2

Due: February 4, Thursday in class Prob. 1 By-hand.

Consider the following finite difference expression to approximate the derivative of a function at x: � � � � � �

� �2 32523

xa xxfxfxxf

'

'���'�

where a is a constant and ǻx is very small. Derive the Taylor series expansions for � �xxf '� 2 and � �xxf '� 3 with base point x, substitute them into the above expression, and answer the following questions.

(a) What derivative is approximated by the expression, e.g., first, second, or third? (b) Determine the constant a. (c) What is the order of the truncation error of this finite difference expression in terms of ǻx?

Prob. 2 Matlab

A traffic light is supported by the cable system as shown. The tensions in the three cables, i.e, TAB, TAC, TAD, are related to the weight W of the traffic light by

0 5 4

7 6

5 3

�� ADACAB TTT

0 5 3

7 3

5 4

�� ADACAB TTT

0 7 2

�WTAB

(a) MATLAB: Create a matrix system and write a MATLAB script file that determines the tensions in the cables for 2000 ddW N with an increment of 1 N, and plot the three tensions vs. W in one plot. [Please use different line types and legends to differentiate the results clearly]

(b) If the maximum tension that can be supported in any of the cables is 500 N, what is the maximum weight of traffic light based on the results in (a) ? Which cable fails first as the weight increases?