# Determening the Period of Coupled Oscillators

by omertech
Tags: coupled, determening, oscillators, period
 P: 13 Hello everyone, I was wondering how could you determine the period of the motion of two or more coupled oscillators. For example, two oscillators have the state variable equations: $$x_1=A_1\cos{(\omega_1t+\phi_1)}+A_2\cos{(\omega_2t+\phi_2)}$$ $$x_2=A_1\cos{(\omega_1t+\phi_1)}-A_2\cos{(\omega_2t+\phi_2)}$$ Thanks!
 P: 13 Thanks for the answer. As far as I know ω1 and ω2 are the angular frequencies. They are related to the periods T1 and T2 by: $$T_1=\frac{2\pi}{\omega_1}$$ $$T_2=\frac{2\pi}{\omega_2}$$ What I am looking for is indeed the repetition period. I know about the common multiple thing, but isn't there any general solution for any oscillation? Because I know that there is a harmonic repetition in coupled oscillations, the question is in what period? Thanks again