# Does ODE initial value problem produce beat or resonance phenomenon? x''+9x=\sin

Does ODE initial value problem produce beat or resonance phenomenon?
$x{}^{″}+9x=\mathrm{sin}\left(3t\right)$
$x\left(0\right)={x}^{\prime }\left(0\right)=0$.
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reinosodairyshm
You are forcing the system at the natural frequency of the system $\left(\omega 0=±3\right)$, so it is unlikely to get a beat (amplitude modulation when the excitation frequency differs from the system modes).
Since there is a t term in the response, the amplitude is unbounded. This is presumably what you call resonance.