Round 1: Tossup 13

The observation that these devices are not isochronous inspired Christiaan Huygens (“HOW-ginz”) to solve the tautochrone (10[1])problem. The period of these devices depends on their initial displacement (10[2])and is proportional (10[1])to an elliptic (10[2]-5[1])integral of the first kind. A coupled pair of these devices is a classic (10[1])example of a chaotic system. (10[1]-5[1])When these devices’ equation of motion is linearized with the small angle approximation, they can be (10[1])approximated as harmonic oscillators whose frequency is the square root of little g over L. The Earth’s rotation causes the precession of a type of these devices named for Léon Foucault (“foo-KOH”). For 10 points, what devices consist of a mass at the end of a rod? ■END■ (10[1])

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