Topic
Simple harmonic motion
About: Simple harmonic motion is a research topic. Over the lifetime, 1653 publications have been published within this topic receiving 29556 citations. The topic is also known as: Free oscillation.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, the authors apply the influence-functional method of Feynman and Vernon to the study of Brownian motion at arbitrary temperature and obtain an explicit expression for the time evolution of the complete density matrix ϱ(x, x, x′, t) when the system starts in a particular kind of pure state.
Abstract: We apply the influence-functional method of Feynman and Vernon to the study of Brownian motion at arbitrary temperature. By choosing a specific model for the dissipative interaction of the system of interest with its environment, we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient. We show that in the limit h→0 the results obtained from the influence functional formalism reduce to the classical Fokker-Planck equation. In the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature, we obtain an explicit expression for the time evolution of the complete density matrix ϱ(x, x′, t) when the system starts in a particular kind of pure state. We compare our results with those of other approaches to the problem of dissipation in quantum mechanics.
2,940 citations
Book•
[...]
1 Jan 1948
TL;DR: In this paper, the Simple Oscillator is described as a simple system with a simple unit function and a simple harmonic motion, and the case of small coupling is discussed, as well as normal modes of vibration.
Abstract: CHAPTER II THE SIMPLE OSCILLATOR 3. Free Oscillations The General Solution. Initial Conditions. Energy of Vibration 4. Damped Oscillations The General Solution. Energy Relations 5. Forced Oscillations The General Solution. Transient and Steady State. Impedance and Phase Angle. Energy Relations. Electromechanical Driving Force. Motional Impedance. Piezoelectric Crystals. 6. Response to Transient Forces Representation by Contour Integrals. Transients in a Simple System. Complex Frequencies. Calculating the Transients. Examples of the Method. The Unit Function. General Transient. Some Generalizations. Laplace Transfoms. 7. Coupled Oscillations The General Equation. Simple Harmonic Motion. Normal Modes of Vibration. Energy Relations. The Case of Small Coupling. The Case of Resonance. Transfer of Energy. Forced Vibrations. Resonance and Normal Modes. Transient Response. Problems
1,205 citations
TL;DR: In this article, a single-degree of freedom non-linear oscillator is considered and the nonlinearity is in the restoring force and is piecewise linear with a single change in slope.
892 citations
29 Jan 1972
TL;DR: In this paper, the derivation of a two-dimensional differential equation, which describes the phenomenon of combined refraction - diffraction for simple harmonic waves, and a method of solving this equation is presented.
Abstract: This paper treats the derivation of a two-dimensional differential equation, which describes the
phenomenon of combined refraction - diffraction for simple harmonic waves, and a method of solving this
equation The equation is derived with the aid of a small parameter development, and the method of
solution is based on the finite element technique, together with a source distribution method
849 citations
TL;DR: In this paper, the equilibrium ground state energies of the 1p shell nuclei are calculated by diagonalizing the full many-particle Hamiltonian with saturating forces in an M, rather than J, Slater determinant representation.
814 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 12 |
| 2024 | 29 |
| 2023 | 59 |
| 2022 | 87 |
| 2021 | 41 |
| 2020 | 46 |