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August 19th, 2009, 10:06 PM   #1
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periodic/not periodic functions- application to electronics

one of the following functions is periodic and the other is not:


f(t) = cos(10(pi)t)+3sin(4(pi)t)
g(t) = cos(10t)+3sin(4(pi)t)


which function is peridic? what is the fundamental period of the function? which is not periodic and why isnt it?
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August 20th, 2009, 05:36 AM   #2
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Re: periodic/not periodic functions- application to electronics

The functions sin(at) and cos(at) are periodic and their period is .
If we look at ,
then we see that the cosine has period ,
and that the sine has period .
Which means that for every 5 periods of the cosine, there are 2 periods of the sine,
and hence it's also 1 period of the sum, f(t). The length of this period is then 1.
But if we look at ,
the period of the cosine is and that of the sine is .
In this case, we can't say that a whole number of periods of the cosine is equal to a whole number of periods of the sine.
Hence we can't point out a period for the sum of them, g(t).
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