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The animation below is a simple harmonic oscillator with no damping set into motion. It oscillates indefinitely at it's resonance frequency.
The animation below is a simple harmonic oscillator that has internal damping.
Below are three animations of a simple harmonic oscillator that is driven below it's resonance frequency (0.6*f_0) for a few cycles, at it's resonance frequency for a few cycles, and then above its resonance frequency (1.4*f_0) for a few cycles.
Below resonance:

At resonance:

Above resonance:
