For the sum to be periodic, $f_1$ and $f_2$ must be commensurable; that is, there most be a number $f_0$ contained in each an integral number of times. Thus, if $f_0$ is the largest such number, $f_1$=$n_1 f_0$ and $f_2=n_2 f_0$ ($f_0$ is the fundamental frequency and $n_1$ and $n_2$ are integers) Which of the signals are periodic:
a) $x_1(t)=2 \cos(2t) + 3\sin(5\pi t)$
b) $x_2(t)=2 \cos(4\pi t) + 5\cos(6\pi t) + 6\sin(22\pi t)$
Find the period of those that are periodic.
How can I find $f_0$? I have an idea but I don't know if it's correct for:
a) We know that $\cos(2t)$ is $\cos wt$, where $w=2\pi f$ so $f_1$ would be $f_1=2/(2\pi)=0.318$ for $3\sin(5\pi t)$, $f_2=2.5$. But how do I find $f_0$ if I don't have $n_1$ or $n_2$??? After that I'm block... what am I missing?
Thanks for your help