The pendulum oscillates harmonically when displacements from equilibrium are small. Motion turns dramatically chaotic and unpredictable when displacements are large.

Timestamps:
00:04 Harmonic Motion Stage 1
00:18 Harmonic Motion Stage 2
00:33 Harmonic Motion Stage 3
00:55 Chaotic Motion Stage 1
01:39 Chaotic Motion Stage 2
02:40 Chaotic Motion Stage 3

"The extreme sensitivity of future behavior to small differences at early times is a characteristic of chaotic systems. This extreme sensitivity also affects predictions. Even if the theoretical model is perfect in every detail, the future behavior of a chaotic system is unpredictable because the starting conditions for the model can never be 100% accurate.

For example, the chaotic nature of weather makes accurate long-term forecast impossible. To predict the future weather, the current conditions are used as input. Any small difference between the true current conditions and those used as input will grow to huge errors in the forecast later on." University of Florida, Department of Physics, demo of Chaotic Pendulum.

Check out uncoupled Wave Pendulum which glows in the dark: [ Ссылка ]

Watch other chaotic and coupled pendulums in action at:

Lego Coupled Pendulums with Magnets: [ Ссылка ]
Double Pendulum Displays Chaotic Motion: [ Ссылка ]
Double Pendulum Chaotic Gymnastics: [ Ссылка ]
Rott’s Chaotic Pendulum: [ Ссылка ]
Double Pendulum Chaotic Acrobatics: [ Ссылка ]
Chaotic Motion with Two Coupled Pendulums in Resonance: [ Ссылка ]

Reference: Make magazine Volume 22, June 2010.

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