\[ \begin{align}\begin{aligned}\newcommand\blank{~\underline{\hspace{1.2cm}}~}\\% Bold symbols (vectors) \newcommand\bs[1]{\mathbf{#1}}\\% Differential \newcommand\dd[2][]{\mathrm{d}^{#1}{#2}} % use as \dd, \dd{x}, or \dd[2]{x}\\% Poor man's siunitx \newcommand\unit[1]{\mathrm{#1}} \newcommand\num[1]{#1} \newcommand\qty[2]{#1~\unit{#2}}\\\newcommand\per{/} \newcommand\squared{{}^2} \newcommand\cubed{{}^3} % % Scale \newcommand\milli{\unit{m}} \newcommand\centi{\unit{c}} \newcommand\kilo{\unit{k}} \newcommand\mega{\unit{M}} % % Percent \newcommand\percent{\unit{{\kern-4mu}\%}} % % Angle \newcommand\radian{\unit{rad}} \newcommand\degree{\unit{{\kern-4mu}^\circ}} % % Time \newcommand\second{\unit{s}} \newcommand\s{\second} \newcommand\minute{\unit{min}} \newcommand\hour{\unit{h}} % % Distance \newcommand\meter{\unit{m}} \newcommand\m{\meter} \newcommand\inch{\unit{in}} \newcommand\foot{\unit{ft}} % % Force \newcommand\newton{\unit{N}} \newcommand\kip{\unit{kip}} % kilopound in "freedom" units - edit made by Sri % % Mass \newcommand\gram{\unit{g}} \newcommand\g{\gram} \newcommand\kilogram{\unit{kg}} \newcommand\kg{\kilogram} \newcommand\grain{\unit{grain}} \newcommand\ounce{\unit{oz}} % % Temperature \newcommand\kelvin{\unit{K}} \newcommand\K{\kelvin} \newcommand\celsius{\unit{{}^\circ C}} \newcommand\C{\celsius} \newcommand\fahrenheit{\unit{{}^\circ F}} \newcommand\F{\fahrenheit} % % Area \newcommand\sqft{\unit{sq\,\foot}} % square foot % % Volume \newcommand\liter{\unit{L}} \newcommand\gallon{\unit{gal}} % % Frequency \newcommand\hertz{\unit{Hz}} \newcommand\rpm{\unit{rpm}} % % Voltage \newcommand\volt{\unit{V}} \newcommand\V{\volt} \newcommand\millivolt{\milli\volt} \newcommand\mV{\milli\volt} \newcommand\kilovolt{\kilo\volt} \newcommand\kV{\kilo\volt} % % Current \newcommand\ampere{\unit{A}} \newcommand\A{\ampere} \newcommand\milliampereA{\milli\ampere} \newcommand\mA{\milli\ampere} \newcommand\kiloampereA{\kilo\ampere} \newcommand\kA{\kilo\ampere} % % Resistance \newcommand\ohm{\Omega} \newcommand\milliohm{\milli\ohm} \newcommand\kiloohm{\kilo\ohm} % correct SI spelling \newcommand\kilohm{\kilo\ohm} % "American" spelling used in siunitx \newcommand\megaohm{\mega\ohm} % correct SI spelling \newcommand\megohm{\mega\ohm} % "American" spelling used in siunitx % % Capacitance \newcommand\farad{\unit{F}} \newcommand\F{\farad} \newcommand\microfarad{\micro\farad} \newcommand\muF{\micro\farad} % % Inductance \newcommand\henry{\unit{H}} \newcommand\H{\henry} \newcommand\millihenry{\milli\henry} \newcommand\mH{\milli\henry} % % Power \newcommand\watt{\unit{W}} \newcommand\W{\watt} \newcommand\milliwatt{\milli\watt} \newcommand\mW{\milli\watt} \newcommand\kilowatt{\kilo\watt} \newcommand\kW{\kilo\watt} % % Energy \newcommand\joule{\unit{J}} \newcommand\J{\joule} % % Composite units % % Torque \newcommand\ozin{\unit{\ounce}\,\unit{in}} \newcommand\newtonmeter{\unit{\newton\,\meter}} % % Pressure \newcommand\psf{\unit{psf}} % pounds per square foot \newcommand\pcf{\unit{pcf}} % pounds per cubic foot \newcommand\pascal{\unit{Pa}} \newcommand\Pa{\pascal} \newcommand\ksi{\unit{ksi}} % kilopound per square inch \newcommand\bar{\unit{bar}} \end{aligned}\end{align} \]

Dec 04, 2025 | 492 words | 5 min read

16.2.2. Task 2

Learning Objectives

Read code with user defined functions. Create user defined functions in MATLAB.

Task Instructions

Part A: Tracking User Defined Functions through MATLAB Code

The following exercise is to be worked on as a team in-class. Work with the problems by hand first and then type the solutions into MATLAB to check them. Be prepared to show a member of the instructional team after you find the correct solutions. When you are finished, write your answer in ma2_team_2_teamnumber.pdf and save the file.

Consider the user-defined functions, fn1 and fn2, as shown below.

function [x,y]=fn1(x,y)
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Help description
%%%%%%%%%%%%%%%%%%%%%%%%%%%
x = x - 4;
[y,x] = fn2(x,y);
y = x^2 - 10;
end

function [out1,out2]=fn2(in1,in2)
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Help description
%%%%%%%%%%%%%%%%%%%%%%%%%%%
out1 = in1 + in2;
out2 = in2 - in1;
end

The following codes are executed in the MATLAB Command window. What values do the variables x and y have?

>> x = 3;
>> y = 5;
>> [x,y] = fn1(x,y)

Part B: Creating User Defined Functions in MATLAB

Open up the following document: (ma2_Team_2_teamnumber.docx)

In the following exercise, you will create three user-defined functions that will be used in Task #3 of this assignment. The background of these functions is explained in Task #3, but is not needed to complete this task. These functions will be created in three different MATLAB files using the MATLAB UDF file template, ENGR133_MATLAB_UDF_Template.m.

The geometric parameters of a blind are:

• \(S\) = slat spacing (\(\milli\meter\))

• \(W\) = slat width (\(\milli\meter\))

• \(M\) = width of slat that is illuminated (\(\milli\meter\))

• \(\Psi\) = slat angle with horizontal (given in degrees)

• \(\sigma\) = vertical shadow angle (given in degrees)

Additionally, the blind surface material has an absorptivity constant, \(\alpha\) (alpha). This is a dimensionless value between \(0\) and \(1\).

User-Defined Function 1:

Create a UDF named ma2_team_2_fractions_teamnumber.m that calculates and returns the three fraction values \(F_1\), \(F_2\), and \(F_3\) in a vector as [F1, F2, F3]. The inputs to this function are \(S\), \(W\), and \(\Psi\).

\[F_1 = \frac{1}{2} \left( 1 + \frac{S}{W} - \sqrt{1 + \left( \frac{S}{W} \right)^2 + 2\frac{S}{W}\sin{(\Psi)}} \right)\]

\[F_2 = \frac{1}{2} \left( \sqrt{1 + \left( \frac{S}{W} \right)^2 + 2\frac{S}{W}\sin{(\Psi)}} + \sqrt{1 + \left( \frac{S}{W} \right)^2 - 2\frac{S}{W}\sin{(\Psi)}} - 2\frac{S}{W} \right)\]

\[F_3 = \frac{1}{2} \left( 1 + \frac{S}{W} - \sqrt{1 + \left( \frac{S}{W} \right)^2 - 2\frac{S}{W}\sin{(\Psi)}} \right)\]

Publish this file as ma2_team_2_fractions_pub_teamnumber.pdf

Sample Output

Use the values in Table 16.3 below to test your program.

Table 16.3 Test Cases

Case	\(S\)	\(W\)	\(\Psi\)
1	40	50	30

Ensure your program’s output matches the provided samples exactly. This includes all characters, white space, and punctuation. In the samples, user input is highlighted like this for clarity, but your program should not highlight user input in this way.

Case 1 Sample Output

>> ma2_team_2_ma2_team_2_fractions_teamnumber(40, 50, 30)

ans =

0.1190 0.4393 0.4417

User-Defined Function 2:

Create a UDF named ma2_team_2_transmission_teamnumber.m that calculates and returns \(T_D\). The inputs to this function are a vector containing \([F_1, F_2, F_3]\), and the geometric parameters \(S\), \(W,\) \(\Psi\), \(\alpha\), and \(\sigma\).

\[T_D = 1 - \frac{W}{S}\frac{\sin{( \sigma + \Psi )}}{\cos{( \sigma )}} \left( 1 - F_1(1-\alpha) - \frac{ F_2 (1 - \alpha)^2 [F_3 + F_1 \cdot F_2 (1 - \alpha)] }{ 1 - F_2^2 (1 - \alpha)^2 } \right)\]

Publish this file as ma2_team_2_transmission_pub_teamnumber.pdf

Sample Output

Use the values in Table 16.4 below to test your program.

Table 16.4 Test Cases

Case	[F1, F2, F3]	\(S\)	\(W\)	\(\Psi\)	\(\alpha\)	\(\sigma\)
1	[0.119, 0.4393, 0.4417]	40	50	30	0.5	18

Ensure your program’s output matches the provided samples exactly. This includes all characters, white space, and punctuation. In the samples, user input is highlighted like this for clarity, but your program should not highlight user input in this way.

Case 1 Sample Output

>> ma2_team_2_ma2_team_2_transmission_teamnumber([0.119, 0.4393, 0.4417], 40, 50, 30, 0.5, 18)

ans =

0.1341

User-Defined Function 3:

Create a UDF named ma2_team_2_absorb_teamnumber.m that calculates and returns \(A_D\). The inputs to this function are \(F_2\), \(S\), \(W\), \(\Psi\), \(\alpha\), and \(\sigma\).

\[A_D = \frac{\alpha W \sin{(\sigma + \Psi)}}{S \cos{(\sigma)}[1 - F_2(1-\alpha)]}\]

Publish this file as ma2_team_2_absorb_teamnumber.pdf

Sample Output

Use the values in Table 16.5 below to test your program.

Table 16.5 Test Cases

Case	\(F_2\)	\(S\)	\(W\)	\(\Psi\)	\(\alpha\)	\(\sigma\)
1	0.4393	40	50	30	0.5	18

Ensure your program’s output matches the provided samples exactly. This includes all characters, white space, and punctuation. In the samples, user input is highlighted like this for clarity, but your program should not highlight user input in this way.

Case 1 Sample Output

>> ma2_team_2_ma2_team_2_absorb_teamnumber(0.4393, 40, 50, 30, 0.5, 18)

ans =

0.6258

Table 16.6 Deliverables

Deliverables	Description
ma2_team_2_fractions_teamnumber.m	Your completed MATLAB code.
ma2_team_2_transmission_teamnumber.m	Your completed MATLAB code.
ma2_team_2_absorb_teamnumber.m	Your completed MATLAB code.
ma2_team_2_fractions_pub_teamnumber.pdf	PDF with published MATLAB code
ma2_team_2_transmission_pub_teamnumber.pdf	PDF with published MATLAB code
ma2_team_2_absorb_teamnumber.pdf	PDF with published MATLAB code
ma2_team_2_teamnumber.pdf	Your answers for part A of this task.