A geometric description for simple and damped harmonic oscillators | Zendy

Z. Ok Bayrakdar | Zendy; T. Bayrakdar | Zendy

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A geometric description for simple and damped harmonic oscillators

Author(s) -

Z. Ok Bayrakdar,

T. Bayrakdar

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1902-73

Subject(s) - mathematics , mathematical analysis , harmonic oscillator , curvature , simple (philosophy) , manifold (fluid mechanics) , sectional curvature , oscillation (cell signaling) , simple harmonic motion , scalar (mathematics) , riemannian manifold , harmonic , work (physics) , scalar curvature , classical mechanics , geometry , physics , quantum mechanics , engineering , genetics , mechanical engineering , philosophy , epistemology , biology

In this work we consider the Riemannian geometry associated with the differential equations of one dimensional simple and damped linear harmonic oscillators. We show that the sectional curvatures are completely determined by the oscillation frequency and the friction coefficient and these physical constants can be thought as obstructions for the manifold to be flat. Moreover, equations of simple and damped harmonic oscillators describe nonisomorphic solvable Lie groups with nonpositive scalar curvature.

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