I have a function
$$x(t) = \pi\cos(21\omega_0t)+0.1\cos(39\omega_0t)$$
that I want to solve T from the periodicity identity, $x(t)=x(t+T)$.
What I have tried now is basically just solving $x(t)=x(t+T)$, but this gets really complex. So I tried to do the laplace transform of the function in order to maybe find out a way of solving it more simple, the laplace transform is,
$$X(s) = \pi \frac{s}{s^2+(21\omega_0)^2}+0.1\frac{s}{s^2+(39\omega_0)^2}$$
What struck me here is that I do not really know how to find the periodicity when I am in the frequency plane. I get a feeling it should be a better way of doing it than the latter, but how?