Resonance
Consider an undamped system exhibiting simple harmonic motion. In the real world, we never truly have an undamped system; -some damping always occurs. For theoretical purposes, however, we could imagine a spring-mass system contained in a vacuum chamber. With no air resistance, the mass would continue to move up and down indefinitely.
The frequency of the resulting motion, given by
2. Now suppose this system is subjected to an external force given by
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