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Solved Programming Problems 1.25 Write a program that prints the first sentence of the Gettysburg Address.

Fig. 12-27

Essentially, all that we need to do here is use a sequence of output statements, sending pieces of the sentence to the cou t object:

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Rp 1 Q2 p #

// Prints the first sentence of the Gettysburg Address: main0 -t tout << "\tFourscore and seven years ago our fathers\n"; tout << "brought forth upon this continent a new nation,\n"; tout << "conceived in liberty, and dedicated to the\n"; tout << "proposition that all men are created equal.\n"; return 0;

1 Rs 1 Q2 s !Cs Rs 2 Cs Cs Cp 1 !Cs Rs 2 1 1=Qs 2 Again, the equivalence depends on the operating frequency.

cou t, like this:

Thus, the series contains no cosine terms. Proceeding with the evaluation integral for the sine terms, 2 1 V sin n!t d !t V sin n!t d !t bn 0 ( 2 ) V 1 1 cos n!t cos n!t n n 0 V 2V cos n cos 0 cos n2 cos n 1 cos n n n The series for the square wave is

"\tFourscore and seven years ago our fathers\n" "brought forth upon this continent a new nation,\n" "conceived in liberty, and dedicated to the\n" "proposition that all men are created equal.\n";

CHAP. l]

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The line spectrum for this series is shown in Fig. 17-19. This series contains only odd-harmonic sine terms, as could have been anticipated by examination of the waveform for symmetry. Since the wave in Fig. 17-18 is odd, its series contains only sine terms; and since it also has half-wave symmetry, only odd harmonics are present.

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If you want the output lines to be longer (or shorter) than the individual pieces sent to the output stream, simply adjust your placement of the endline characters 6\n . . #include // Prints main0 <iostream.h> the first sentence of the Gettysburg Address:

Find the trigonometric Fourier series for the triangular wave shown in Fig. 17-20 and plot the line spectrum.

"\tFourscore and seven years ago our fathers "; tout << "brought forth upon\nthis continent a new nation, tout << "conceived in liberty, and dedicated\nto the "; tout << "proposition that all men are created equal.\n"; return 0;

The wave is an even function, since f t f t , and if its average value, V=2, is subtracted, it also has half-wave symmetry, that is, f t f t . For < !t < 0, f t V V= !t; and for 0 < !t < , f t V V= !t. Since even waveforms have only cosine terms, all bn 0. For n ! 1, 1 0 1 V V= !t cos n!t d !t V V= !t cos n!t d !t an 0 0 V !t !t cos n!t d !t cos n!t d !t cos n!t d !t 0 ( 0 ) V 1 !t 1 !t sin n!t sin n!t 2 cos n!t 2 cos n!t n n2 n 0 V 2V cos 0 cos n cos n cos 0 2 2 1 cos n 2 n2 n

Write a program that prints the sum, difference, product, quotient, and remainder of two integers. Initialize the integers with the values 60 and 7.

As predicted from half-wave symmetry, the series contains only odd terms, since an 0 for n 2; 4; 6; . . . . For n 1; 3; 5; . . . ; an 4V= 2 n2 . Then the required Fourier series is f t V 4V 4V 4V cos !t cos 3!t cos 5!t 2 2 3 2 5 2

After declaring integers m and n andi nitializing them with the values 60 and 7, we use one ouput statement to print their values, and then one output statement for each of the five operations: #include <iostream.h>

The coe cients decrease as 1=n2 , and thus the series converges more rapidly than that of Problem 17.1. This fact is evident from the line spectrum shown in Fig. 17-21.

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