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A device or circuit that generates an AC signal at a certain frequency.

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Why don't infinitely many sinusoidals exist in an oscillator circuit?

Consider a new osciallation n sin (wt + theta) - to a constant factor / phase the oscillator sees (sin wt) + n sin (wt + theta) - another sine wave. … Therefore we can imagine that such an oscillator must reject large gain in the new wave. …
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