My Math Forum periodic/not periodic functions- application to electronics

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 August 19th, 2009, 10:06 PM #1 Newbie   Joined: May 2009 Posts: 20 Thanks: 0 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?
 August 20th, 2009, 05:36 AM #2 Member   Joined: Jul 2009 Posts: 34 Thanks: 0 Re: periodic/not periodic functions- application to electronics The functions sin(at) and cos(at) are periodic and their period is $2\pi/a$. If we look at $f(t)=cos(10\pi t)+3sin(4\pi t)$, then we see that the cosine has period $\frac{2\pi}{10\pi}=\frac{1}{5}$, and that the sine has period $\frac{2\pi}{4\pi}=\frac{1}{2}$. 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 $g(t)=cos(10t)+3sin(4\pi t)$, the period of the cosine is $\frac{2\pi}{10}=\frac{1}{5}\pi$ and that of the sine is $\frac{2\pi}{4\pi}=\frac{1}{2}$. 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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