Christiaan Huygens invented a type of clock that uses one of these devices, whose period is proportional to the square root of the length of the pivot. For 10 points each:
[10e] Name these simple harmonic oscillators that consist of a bob on the end of a pivot like a string.
ANSWER: pendulums
[10m] A double pendulum is a common illustration of this phenomenon, in which a system is highly sensitive to changes in initial conditions.
ANSWER: chaos [or chaotic; accept word forms]
[10h] The equations of motion for a double pendulum, or any pendulum, can be calculated by first computing this quantity, which is the difference between a system’s kinetic energy and potential energy.
ANSWER: Lagrangian [prompt on L]
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