Harmonic Oscillator Potential to describe Internal Dissipation

Oscillator damping with more than one mechanism of internal friction dissipation

The author's modified Coulomb damping model has been generalized to accommodate internal friction that derives from several dissipation mechanisms acting simultaneously. Because of its fundamental nonlinear nature, internal friction damping causes the quality factor Q of an oscillator in free-decay to change in time. Examples are given which demonstrate reasonable agreement between theory and experiment.

Fractional Oscillator -- Harmonic Oscillator with Memory Effects

The importance of fractional time-derivative to take care of memory effects has been brought out by considering the example of a simple oscillator.

Slow-dissipation limit of the harmonic oscillator with general power-law damping

An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to investigate amplitude decay in the presence of general types of weak, nonlinear damping.

Condition for minimal Harmonic Oscillator Action

We provide an elementary proof that the action for the physical trajectory of the one-dimensional harmonic oscillator is guaranteed to be a minimum if and only if $τ< π/ω$, where $τ$ is the elapsed time and $ω$ is the oscillator's natural frequency.

Shock Waves in Falling Coupled Harmonic Oscillators

Shock waves propagate in falling coupled harmonic oscillators. The bottom end of coupled harmonic oscillators does not fall downwards until a shock wave reaches the bottom end. The exact solution can be expressed by the Fourier series expansion, and an approximate solution can be expressed by the integral of the Airy function. The width of the shock wave increases slowly in accordance with a power law.

具有时间依赖频率的相对论线性谐振子的精确不变量

An Exact Invariant for Relativistic Linear Harmonic Oscillator with Time-dependent Frequency

本文通过关联相对论平面各向同性谐振子，构造了时间依赖频率的相对论线性谐振子的精确不变量，并分析了相对论效应对其物理解释的影响。