Concept explainers
Interpretation:
To explain the paradox that a simple harmonic oscillator oscillates along one dimension, but as per the textbook, it is not possible for a one-dimensional system to oscillate.
Concept Introduction:
Dynamics of the first-order system is dominated by fixed points. All the trajectories are either approach to a fixed point or diverge from the fixed points making them either stable or unstable fixed points.
It simply means that the phase points never reverse their direction.
However, if a fixed point is considered as an equilibrium solution, the approach to the equilibrium solution is always monotonic. Therefore, it is not possible to have overshoot or damped or undamped oscillations. Hence, for
Therefore, as per the book, it is not possible for a one-dimensional system to oscillate.
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Check out a sample textbook solutionChapter 2 Solutions
Nonlinear Dynamics and Chaos
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,