We consider small oscillations of micro-particles and gaseous bubbles in a viscous fluid around equilibrium states under the action of a sinusoidal external force. Exact solutions to the governing integro-differential equations containing both Stokes and memory-integral drag forces are obtained. The main aim of this study is to clarify the influence of the memory-integral drag force on the resonance characteristics of oscillating particles or gaseous bubbles in a viscous fluid at small Reynolds numbers. The resonant curves (the amplitude versus the frequency of an external force) and phase-frequency dependences are obtained for both these objects and compared with the corresponding dependences of the traditional oscillator with the Stokes drag force only.

中文翻译：

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粘性流体中粒子和气泡在小雷诺数下强制振荡的共振特性

我们考虑在正弦外力的作用下，围绕平衡状态的粘性流体中的微粒和气泡的微小振荡。获得包含斯托克斯和记忆积分阻力的控制积分微分方程的精确解。本研究的主要目的是阐明记忆积分阻力对小雷诺数下粘性流体中振荡粒子或气泡的共振特性的影响。获得了这两个物体的共振曲线（外力的振幅与频率的关系）和相位频率相关性，并与仅具有斯托克斯阻力的传统振荡器的相应相关性进行了比较。