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Consider the general forced harmonic oscillator:

$$\begin{equation} y''(t) + \omega_0^2 y(t) = \cos \omega t \end{equation}$$

...for some constants $\omega_0$ and $\omega$. Which one of these statements is FALSE?

Resonance occurs when $\omega = \omega_0$

$\omega_0$ is called the natural frequency of the system

No solutions for $y(t)$ exist when $\omega = \omega_0$

Solutions grow in time when $\omega = \omega_0$

There are no periodic solutions when $\omega = \omega_0$

When $\omega \neq \omega_0$, solutions are bounded for all time