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. 2015 Jul 23:5:11548.
doi: 10.1038/srep11548.

Huygens synchronization of two clocks

Henrique M Oliveira  1 , Luís V Melo  2
Affiliations

Huygens synchronization of two clocks

Henrique M Oliveira et al. Sci Rep. .

Abstract

The synchronization of two pendulum clocks hanging from a wall was first observed by Huygens during the XVII century. This type of synchronization is observed in other areas, and is fundamentally different from the problem of two clocks hanging from a moveable base. We present a model explaining the phase opposition synchronization of two pendulum clocks in those conditions. The predicted behaviour is observed experimentally, validating the model.

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Figures

Figure 1
Figure 1. Limit cycle of an isolated clock represented as a solid curve in the phase space.
Horizontal axis represents the angular position and in the vertical axis the velocity. We use normalized coordinates to get arcs of circles.
Figure 2
Figure 2. Interaction of clock 1 on clock 2 at t = 0+.
We see the original limit cycle, before interaction, and the new one in solid and the original limit cycle in dashed. Note that the value of α and of h are greatly exaggerated to provide a clear view. The effect of the perturbation is secular and cumulative.
Figure 3
Figure 3. Second interaction. Interaction of clock 2 on clock 1 when clock 2 reaches its impact position.
All the features are similar to the Fig. 2.
Figure 4
Figure 4. Photo of the experimental setup.
The clocks can be seen hanging from the Al rail. The weights are outside of the picture. The cables in the background connect the optical sensors.
Figure 5
Figure 5. Simulations of delay between the two clocks in period units for two frequency differences.
Upper curve (red): ε = 1.5 × 10−4 rad/s. Lower curve (black): ε = 3.0 × 10−3 rad/s. ω = 4.48799 rad/s.
Figure 6
Figure 6. Phase difference between the clocks in period units over more than three days (lower curve in green, right axis) and periods of the two clocks (upper curves, left axis; red for clock 1, black for clock 2).
The initial behaviour corresponds to mechanical stabilization of the clocks during the first few hours of the experiment.
Figure 7
Figure 7. Phase difference between the clocks in period units over more than three days (lower curve in green, right axis) and periods of the two clocks (upper curves, left axis; red for clock 1, black for clock 2).
The initial behaviour corresponds to mechanical stabilization of the clocks during the firs few hours of the experiment. After running for around 250000 periods, clock 2 is stopped, and clock 1 keeps running undisturbed.
See this image and copyright information in PMC

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References

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