In this task you will be given a text passage from a trivia quiz. You should choose the category this question belongs to from these categories: History, Science, Social Science, Fine Arts, Literature. You can only choose one category, so if in doubt, please choose the closest match.

Q: A version of spectroscopy that is free of one form of this effect uses a standing wave to give radiation to a moving atom and is named for its two-photon transition. Due to this effect, atoms observe laser resonance leading to the phenomenon of optical molasses at its namesake cooling limit. Mossbauer spectroscopy uses this effect to modulate the energy of the incident gamma rays. An experiment that used a canal ray tube and a mirror to view light emissions was used to detect the transverse form of this effect, while its relativistic form involves changes equal to the square root of one plus beta over one minus beta. For 10 points, name this shift in the wavelength from a moving source that can be heard by an observer.

A: Science
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Q: In this work, a definition of justice as "what is good for the stronger" is given by Thrasymachus. In this work, a story about the killer of King Candaules of Lydia is used to describe how people are just out of necessity. That story in this work tells of the [*] "Ring of Gyges." This work describes chained prisoners who watch shadows pass before them. This work combines ideas about the "divided line" and the sun into its "Allegory of the Cave." For 10 points, name this work that proposes a government ruled by philosopher kings, a dialogue on government by Plato.

A: Literature
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Q: A system named for Rott features has two of these structures with horizontal SFP and BFPs at stable equilibria. In the phase-space representation for the system, the upper-half of the separatrix shows solutions for these systems starting at their inverted positions. Two coupled ones are commonly used to represent chaotic systems. When their displacements are assumed to be small, the sine theta term in the equation is approximated to theta. Another of these was used to demonstrate the rotation of the earth and was named for Foucault. For 10 points, identify these physical systems which can be used to model simple harmonic motions, and which swing back and forth in some clocks.

A:
Science
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