关键词: 法诺共振, 弹簧振子, 受迫振动

Abstract: Fano resonance which features asymmetric resonant line shape is a general resonance phenomenon occurred in all kinds of physical systems. It originates from quantum physics and the corresponding microscopic image is the interference between a narrow discrete state with a broad continuous state in atomic spectra. In this paper， taking two coupled spring oscillators in classical mechanics as an example and one of the coupled spring oscillators is driven by a periodic external force，a Fano resonance phenomenon which occurred in quantum mechanics is successfully analogized in classical mechanics. By analyzing the dynamic equation of each oscillator and solving their vibration formula rigorously，the relationships between the amplitude and phase of each oscillator and the frequency of the external driving force are obtained. The results show that the oscillator driven by the external force in the coupled system can excite both asymmetric Fano resonance and symmetric Lorentz resonance，while the other oscillator can only excite Lorentz resonance. The derivation and analysis of this paper give readers a deeper understanding of the Fano resonance and its excitation conditions.

Key words: Fano resonance, spring oscillator, forced oscillation