In this post, Alfred Centauri describes the resonance as a phenomenon which appears when 'the energy flow from the driving source is unidirectional' and then shows that this is the case for $\Omega=\omega_0$.

However, we know that the resonance is reached for $\Omega = \omega_0 \sqrt{1 - 2 (\beta / \omega_0)^2}$. Knowing that, why isn't: $\omega_0 \sqrt{1 - 2 (\beta / \omega_0)^2}$ the only frequency at which the power is positive $\forall t$ rather than: $\omega_0 $ (for $\beta\neq0$).

edit: Maybe, it's because the frequency corresponding to the maximum energy transfer isn't the same as the one corresponding to the maximum amplitude...

  • $\begingroup$ It might be a good idea to plot both things, the amplitude and energy to compare their peaks. $\endgroup$
    – nicoguaro
    Jun 18 '19 at 3:13

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