Low Driving Frequency
In this case, the amplitude becomes
The above expression shows that the external driving force acts as a constant static force F0 which pushes the particle to a maximum distance xmax where restoring (elastic) force balances F0, i.e.
In fact, if ω is (too) small, we note that q = – ω2 q is negligible; also q = ω (– A0 sin ω t) is small. Hence, in case of low driving frequency, both acceleration and damping terms are insignificant and equation of motion reduces to
The above analysis shows it is a static interplay between elastic force and external force F (which changes with time), in case of low frequency.
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