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Illustration Example: Different Paths have Different Action

Example: Different Paths have Different Action
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A height-time diagram is shown here as an example. The aim is to correctly describe the time behavior of the height \(h(t)\) of a body thrown vertically upwards. Three conceivable time curves are drawn in, which have a different action \( S[h] \) (in joules seconds). The path with the smallest action (2 joules seconds) corresponds to a parabola and is "chosen" by the thrown body.