Travel Time on a Wavy Path in an Inclined Plane: A Theoretical and Numerical Review
DOI:
https://doi.org/10.24252/al-khazini.v5i2.60867Kata Kunci:
Wavy Path, Inclined Plane, Energy Conservation, Calculus of Variations, Travel TimeAbstrak
This study investigates the influence of path geometry on the travel time of an object on a frictionless inclined plane, focusing on the comparison between straight and undulating (wave-like) paths. Using the principles of energy conservation and variational calculus, a mathematical expression for the travel time along a sinusoidal path is derived. Although the straight path is geometrically the shortest, the analysis shows that certain wave-shaped trajectories can yield a shorter travel time. Numerical evaluations on various amplitude and frequency parameters reveal their critical role in determining efficiency. This work reinforces the relevance of the Brachistochrone principle in theoretical physics education and demonstrates how simple numerical approaches can be utilized to explore optimal trajectories.
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