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Oscillations and resonance are essential topics in physics that can be explored theoretically and experimentally in the classroom or teaching laboratory environments. However, one of the main challenges concerning the experimental study of…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…
In traditional mechanics, harmonic oscillators can be used to measure force, acceleration, or rotation. Herein, we describe a quantum harmonic oscillator based on a penning trapped calcium ion crystal. Similar to traditional oscillators,…
In this work, we present a simple and low-cost experiment designed to study the oscillations of the magnetic field created by a cylindrical magnet under two different conditions: far and short distances from the magnetic sensor. A Taylor…
We design a low-cost, electromagnetically coupled, simple harmonic oscillator and demonstrate free, damped and forced oscillations in an under-graduate (UG) Physics laboratory. It consists of a spring-magnet system that can oscillate inside…
In this paper we investigate a hybrid quantum system comprising a mechanical oscillator coupled via magnetic induced electromotive force to an $LC$ resonator. We derive the Lagrangian and Hamiltonian for this system and find that the…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…
Engineering nano-mechanical quantum systems possessing ultra-long motional coherence times allow for applications in ultra-sensitive quantum sensing, motional quantum memories and motional interfaces between other carriers of quantum…
The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models.…
A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $\omega^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $\omega^2(t)>0$…
It is the purpose of this manuscript to place an illustrative demonstration on the measurement of damped electromagnetic oscillations for a RLC circuit that it is easy to set in any physics laboratory equipped with PASCO technologies and…
Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…
In this work we consider a dynamic system consisting of a damped harmonic oscillator and we formalize a Turing Machine whose definition in terms of states, alphabet and transition rules, can be considered equivalent to that of the…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
We present an experiment conductive to an understanding of both Faraday's law and the properties of the superconducting state. It consists in the analysis of the motion of a superconducting loop moving under the influence of gravity in an…
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…
This paper develops further the semi-classical theory of an harmonic oscillator acted on by a Gaussian white noise force discussed in (arXiv:1508.02379). Here I add to that theory the effects of Brownian damping (friction). Albeit…
We present a kicked harmonic oscillator where the impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom and not by the canonical quantization of a time-dependent Hamiltonian. The ancila is dynamically…