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Programming With M-Files: For-Loop Exercises

Module by: Darryl Morrell

Summary: This module provide several practice exercises on the use of for-loops.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Exercise 1

Frequency is a defining characteristic of many physical phenomena including sound and light. For sound, frequency is perceived as the pitch of the sound. For light, frequency is perceived as color.

The equation of a cosine wave with frequency f f cycles/second is

y=cos2πft y 2 π f t (1)
Create an m-file script to plot the cosine waveform with frequency f=2 f 2 cycles/s for values of t t between 0 and 4.

Exercise 2

Suppose that we wish to plot (on the same graph) the cosine waveform in Exercise 1 for the following frequencies: 0.7, 1, 1.5, and 2. Modify your solution to Exercise 1 to use a for-loop to create this plot.

Solution A

The following for-loop is designed to solve this problem: 

t=0:.01:4;
hold on
for f=[0.7 1 1.5 2]
    y=cos(2*pi*f*t);
    plot(t,y);
end
When this code is run, it plots all of the cosine waveforms using the same line style and color, as shown in Figure 1. The next solution shows one rather complicated way to change the line style and color.

Figure 1: Plot of cosines at different frequencies.
Figure 1 (Fig1.png)

Solution B

The following code changes the line style of each of the cosine plots. 

fs = ['r-';'b.';'go';'y*']; %Create an array of line style strings
x=1; %Initialize the counter variable x
t=0:.01:4;
hold on
for f=[0.7 1 1.5 2]
    y=cos(2*pi*f*t);
    plot(t,y,fs(x,1:end)); %Plot t vs y with the line style string indexed by x
    x=x+1; %Increment x by one
end
xlabel('t');
ylabel('cos(2 pi f t)')
title('plots of cos(t)')
legend('f=0.7','f=1','f=1.5','f=2')
This code produces the plot in Figure 2. Note that this plot follows appropriate engineering graphics conventions-axes are labeled, there is a title, and there is a legend to identify each plot.

Figure 2: Plot of cosines at different frequencies.
Figure 2 (Fig2.png)

Exercise 3

Suppose that you are building a mobile robot, and are designing the size of the wheels on the robot to achieve a given travel speed. Denote the radius of the wheel (in inches) as r r, and the rotations per second of the wheel as w w. The robot speed s s (in inches/s) is related to r r and w w by the equation

s=2πrw s 2 π r w (2)
On one graph, create plots of the relationship between s s and w w for values of r r of 0.5in, 0.7in, 1.6in, 3.2in, and 4.0in.

Exercise 4

Multiple Hypotenuses

Figure 3: Sides of a right triangle.
Figure 3 (RT.png)
Consider the right triangle shown in Figure 3. Suppose you wish to find the length of the hypotenuse c c of this triangle for several combinations of side lengths a a and b b ; the specific combinations of a a and b b are given in Table 1. Write an m-file to do this.
Table 1: Side Lengths
a a b b
1 1
1 2
2 3
4 1
2 2

Solution

This solution was created by Heidi Zipperian: 

a=[1 1 2 4 2]
b=[1 2 3 1 2]
for j=1:5
    c=sqrt(a(j)^2+b(j)^2)
end
A solution that does not use a for loop was also created by Heidi: 
a=[1 1 2 4 2]
b=[1 2 3 1 2]
c=sqrt(a.^2+b.^2)

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