I am looking for a rule to find the time period $T$ for the following function: $$f(t) = A_1sin(\omega_1t+\phi_1) \cdot A_2sin(\omega_2t+\phi_2)$$ with $\omega_1 \neq \omega_2$ and $\frac{\omega_1}{\omega_2} \in \mathbb{N}$.
If there is no such explicit rule, does maybe a rule of thumb exist?
I tried $T = \frac{2\pi}{\lvert \omega_1-\omega_2\rvert}$ as well as $T = \frac{2\pi} {min(\omega_1,\omega_2)}$ but both seem wrong.
I hope you guys can help me.