How to determine the sampling rate of a continuous signal?

Question

Signal processing

Hello, just started learning DSP. I need in accordance with the Kotelnikov theorem to determine the sampling rate for a continuous signal f(t) = 2sin(2pi*10t) + sin(2pi*30t). I don't understand how to do it, can you explain in detail?

Answer 1

Above is a function of a continuous signal, consisting of harmonics, two sinusoids of different periods.
https://nag.ru/articles/article/103332/teorema-kot...
As far as I understand, you need to determine the periods of each of the sinusoids, choose the smaller one. Then, converting to frequency, multiply by 2 to get the minimum sample rate.
Added
In the comments, it was correctly noted that according to the Kotelnikov's Theorem, the minimum sampling frequency should not be exactly 2 times higher, but a little more. Because the inequality is not strict.