Beats are an important natural phenomena caused by the coupling of two vibrations. Specifically, beats result from the temporal superposition of fundamental modes of oscillation. In this demo, a symmetric displacement of the pendulums (upper-right photo) gives rise to one fundamental mode with a long period, $T_1$. An anti-symmetric displacement of the pendulums gives rise to another fundamental mode but with a short period $T_2$ (lower-right photo). Note that in the symmetric mode, the pendulums oscillate independently about the upper bar, and in the anti-symmetric case, they oscillate independently about the lower dowel at mid-length. When the two initial conditions are superposed (shown directly above), the dowel acts to couple these two fundamental or “eigen” modes. In this beat mode, the exchange of energy back and forth between the two pendulums is clearly seen. The amount of time required for this exchange, the beat period, is given by:

$$T_{beat} = \frac{T_1 T_2}{T_1 - T_2}$$