Say I have a sum of two sinusoids like so:
$$
Acos(xt+\phi) + Bcos(yt+\delta)
$$
How would I find the period? I know that for just one sinusoid the period would be:
$$
Acos(xt+\phi)
$$
$$
T = 2\pi/x
$$
It can't be as simple as just adding the two periods.
How can I tell if they're not periodic?
Best Answer
Beware that assuming there is a period to find is a big assumption. For example, suppose your two sinusoids are $\cos{2\pi t}$ and $\cos{\frac{2\pi t}{\sqrt{2}}}$. The periods of the two functions are $1$ and $\sqrt{2}$, respectively. If their sum was periodic, its period would be the least common multiple of $1$ and $\sqrt{2}$, which would allow us to write $\sqrt{2}$ as a ratio of integers (red flag!).