When an oscillator vibrates in a porous medium or along an unsmooth surface, a fractal model can be adopted using the two-scale fractal derivative. This paper elucidates a simple but effective method for fast and exclusive insight into the asymptotically periodic property at the initial stage and the extremely low frequency property when time tends to infinity. Some examples are illustrated to show the one-step solution process and the accurate results.

中文翻译：

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分形振荡及其频率-幅度特性

当振子在多孔介质中或沿不光滑表面振动时，可采用二尺度分形导数建立分形模型。本文阐明了一种简单而有效的方法，可以快速而独到地洞察初始阶段的渐近周期特性和时间趋于无穷大时的极低频特性。举例说明了一步求解过程和准确的结果。