We report the observation and quantitative measurements of the parametric resonance of a two-degree-of-freedom harmonic oscillator made of two coupled pendula. When varying the length of one of the pendula, we parametrically excite the whole set. The frequency of this excitation can be tuned and its depth ajusted, enabling us to draw a frequency-depth Cartesian diagram in which the oscillation behaviour, namely finiteness or exponential divergence, can be plotted. As in the well-known case of the one-degree-of-freedom oscillator, the stability and instability domains are demarcated by a tongue centred at twice the oscillator's free frequency. But in the two-degree-of-freedom oscillator case, this tongue has a three-tip fine structure, two tips corresponding to the free oscillator's eigenfrequencies and an extra tip corresponding to the average of both eigenfrequencies. This situation is unravelled theoretically using a classical adaptation of a formalism introduced in quantum optics by Glauber.

我们报告了观察和定量测量的由两个耦合摆构成的两自由度谐波振荡器的参数共振。当改变一个摆的长度时，我们从参数上激发了整个摆。可以调整该激励的频率并调整其深度，从而使我们能够绘制频率-深度笛卡尔图，在其中可以绘制出振荡行为（即有限度或指数散度）的图表。如同众所周知的单自由度振荡器一样，稳定性和不稳定性域由以振荡器自由频率两倍为中心的舌形划分。但是在二自由度振荡器的情况下，该舌具有三尖端的精细结构，两个尖端对应于自由振荡器的 s本征频率和对应于两个本征频率平均值的额外提示。使用格劳伯（Glauber）在量子光学中引入的形式主义的经典改编，从理论上阐明了这种情况。