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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.
A system obeying the harmonic oscillator equation of motion can be used as a force or proper acceleration sensor. In this short review we derive analytical expressions for the sensitivity of such sensors in a range of different situations, considerin
It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary. Two system
We analyse the charging process of quantum batteries with general harmonic power. To describe the charge efficiency, we introduce the charge saturation and the charging power, and divide the charging mode into the saturated charging mode and the unsa
Let $H$ denote the harmonic oscillator Hamiltonian on $mathbb{R}^d,$ perturbed by an isotropic pseudodifferential operator of order $1.$ We consider the Schrodinger propagator $U(t)=e^{-itH},$ and find that while $operatorname{singsupp} operatorname{
Thermodynamic fluctuations in mechanical resonators cause uncertainty in their frequency measurement, fundamentally limiting performance of frequency-based sensors. Recently, integrating nanophotonic motion readout with micro- and nano-mechanical res