OPAC - Pencarian Artikel Jurnal & Majalah Library USD
Menampilkan semua artikel (Halaman 781 dari 34166, Total: 341652 data)
Why the action
klik untuk membaca file PDF
| Pengarang | : | Keith Zengel |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 885-888 |
| Abstrak | : | In this note, I present two variations of the principle of stationary action in order to provide alternative ways for students to think about the action that they may find more intuitive than the traditional approach. These methods involve Lagrange multiplier techniques and are, therefore, best suited for students who are encountering the stationary action principle for a second or third time, perhaps in an advanced undergraduate mathematical methods course or a graduate classical mechanics course. |
A simple model of a gravitational lens from geometric optics
| Pengarang | : | Bogdan Szafraniec; James F. Harford |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 878-884 |
| Abstrak | : | We propose a simple geometric optics analog of a gravitational lens with a refractive index equal to one at large distances and scaling like ?(?)2=1+?2/?2?, where C is a constant. We obtain the equation for ray trajectories from Fermat's principle of least time and the Euler equation. Our model yields a very simple ray trajectory equation. The optical rays bending, reflecting, and looping around the lens are all described by a single trigonometric function in polar coordinates. Optical rays experiencing fatal attraction are described by a hyperbolic function. We use our model to illustrate the formation of Einstein rings and multiple images. |
Revisiting Sommerfelds atomic model using Euler Lagrange dynamics
| Pengarang | : | Suwarno, B. Djoko Untoro |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 872-877 |
| Abstrak | : | The purpose of this work is to present the atomic model proposed by Sommerfeld. We outline the classical calculation of the elliptical orbit and then apply the Wilson–Sommerfeld quantization rules to obtain expressions for the quantization of energy and orbit semi-axes. We then apply the relativistic theory to solve the problem of degenerate orbits. Thus, we see that the Sommerfeld atom is a very rich topic, involving the integration of different subjects ranging from Lagrangian mechanics to relativity, as well as plane geometry and differential equations. |
Analytical solution of the Sommerfeld Page equation
| Pengarang | : | Zurab K. Silagadze |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 864-871 |
| Abstrak | : | The Sommerfeld–Page equation describes the non-relativistic dynamics of a classical electron modeled by a sphere of finite size with a uniform surface charge density. It is a delay differential equation, and almost no exact solution of this equation was known until recently. However, progress has been made, and an analytical solution was recently found for an almost identical delay differential equation, which arose in the context of the mathematical modeling of the COVID-19 epidemics. Inspired by this research, we offer a pedagogical exposition of how one can find an analytical solution of the Sommerfeld–Page equation. |
Kramers Kronig relations via Laplace formalism and L1 integrability
| Pengarang | : | Marco Prevedelli; Alessio Perinelli; Leonardo Ricci |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 859-863 |
| Abstrak | : | Kramers–Kronig relations link the real and imaginary parts of the Fourier transform of a well-behaved causal transfer function describing a linear, time-invariant system. From the physical point of view, according to the Kramers–Kronig relations, absorption and dispersion become two sides of the same coin. Due to the simplicity of the assumptions underlying them, the relations are a cornerstone of physics. The rigorous mathematical proof was carried out by Titchmarsh in 1937 and just requires the transfer function to be square-integrable (L2), or equivalently that the impulse response of the system at hand has a finite energy. Titchmarsh's proof is definitely not easy, thus leading to crucial steps that are often overlooked by instructors and, occasionally, prompting some authors to attempt shaky shortcuts. Here, we share a rigorous mathematical proof that relies on the Laplace formalism and requires a slightly stronger assumption on the transfer function, namely it being Lebesgue-integrable (L1). While the result is not as general as Titchmarsh's proof, its enhanced simplicity makes a deeper knowledge of the mathematical aspects of the Kramers–Kronig relations more accessible to the audience of physicists. |
Playing with active matter
| Pengarang | : | Angelo Barona Balda; Aykut Argun; Agnese Callegari; Giovanni Volpe |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 847-858 |
| Abstrak | : | In the past 20 years, active matter has been a very successful research field, bridging the fundamental physics of nonequilibrium thermodynamics with applications in robotics, biology, and medicine. Active particles, contrary to Brownian particles, can harness energy to generate complex motions and emerging behaviors. Most active-matter experiments are performed with microscopic particles and require advanced microfabrication and microscopy techniques. Here, we propose some macroscopic experiments with active matter employing commercially available toy robots (the Hexbugs). We show how they can be easily modified to perform regular and chiral active Brownian motion and demonstrate through experiments fundamental signatures of active systems such as how energy and momentum are harvested from an active bath, how obstacles can sort active particles by chirality, and how active fluctuations induce attraction between planar objects (a Casimir-like effect). These demonstrations enable hands-on experimentation with active matter and showcase widely used analysis methods. |
Elastic collisions on a simulated circular air track
| Pengarang | : | C. B. Price; M. L. Pethybridge |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 841-846 |
| Abstrak | : | Elastic collisions of gliders on linear air tracks are often used to explore conservation of energy and momentum. If one is interested in the glider behavior over a long time span, the analysis involves repeated collisions and is complicated by reflections from the track end stops. Here we analyze elastic collisions on a novel circular air track; since such a track lacks end stops, the mathematical analysis of repeated collisions is amenable to our students. Our analysis uncovers a variety of interesting behaviors which depend on the ratio of the glider masses. We examine periodic sequences where the gliders return to their initial conditions and progressions where (when plotted in polar coordinates) the collision positions take on the locus of a spiral. One set of initial conditions produces an “angle trap” where one glider remains within a certain angular range. We also explore making one glider's mass hypothetically negative, which results in a novel “chasing” motion. Our results were obtained using a 3D interactive simulation (created using C++ within the Unreal engine), which we make available as supplementary material. |
The hardest-hit home run
| Pengarang | : | Donald C. Warren |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 834-840 |
| Abstrak | : | We present a problem to be assigned or done as an in-class activity in an upper-division undergraduate course on computational physics. The problem involves a home run hit by Mickey Mantle on May 22, 1963, which he famously called “the hardest ball I ever hit.” Is this home run truly one for the record books, or has it been eclipsed by players in the modern era? Modeling the trajectory of a baseball involves consideration of both wind resistance and the Magnus effect and is an interesting application of numerical solutions to ordinary differential equations. Ultimately, the answer is that Mantle would compare favorably to the most powerful batters currently playing, but to arrive at that conclusion we must reflect on the plausibility of results and sources of uncertainty. |
On cat–human interaction from the viewpoint of physics: An equation of motion
| Pengarang | : | Anxo Biasi |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 11) |
| Halaman | : | 827-833 |
| Abstrak | : | This paper provides an enjoyable example through which several concepts of classical mechanics can be understood. We introduce an equation that models the motion of a cat in the presence of a person. The cat is considered as a point particle moving in a potential induced by the person. We demonstrate that this approach to the problem reproduces characteristic behaviors of these curious animals. For instance, the fact that cats do not typically come when they are called, or that they remain longer on the lap of their favorite person; even “zoomies” are reproduced (cats randomly run back and forth across the house). We use this model problem to explore topics of current research such as stochastic equations and periodically driven systems. The pedagogical value of this work and its potential use in teaching are discussed. |
Flipping the electronics lab: Learning upper division electronics at home
| Pengarang | : | Brian Rasnow |
| Nama Majalah/Jurnal | : | American Journal of Physics |
| Volume / Edisi | : | 92 (No. 10) |
| Halaman | : | 809-818 |
| Abstrak | : | A junior-level four-unit electronics curriculum is described in which students learn by building their own automated electronic test equipment and performing a rigorous suite of electronics experiments outside the classroom. Each student builds an electronics “workbench” based on an Arduino Nano microcontroller under the control of a software scripting environment (in our case, MATLAB). In the course of their work, students (1) construct a DC power supply and function generator and iteratively add programmable serial interfaces; (2) create an oscilloscope and spectrum analyzer that provides real-time displays of two analog channels for measurement of AC voltage amplitudes, frequency, and phase difference; (3) automate measurements of device I–V curves and transistor gain; (4) design, build, and characterize audio amplifiers and filters through measurement of time constants and frequency responses; and (5) compare the measured and simulated Bode plots. Mixing unconventional topics such as automation, numerical simulation, and programming with basic electronics removes the drudgery of data collection and provides more exposure, repetition, and organization of key concepts. Without being restricted to making measurements within the imposed lab schedule, students can work where and when they are able, repeat automated experiments in seconds, and continue exploring electronics with their workbench. After completing this course, our students demonstrate more confidence and capability with integrating electronics, automation, and programming into other projects and in improving existing systems. Likewise, students glean hands-on experience with scripting repetitive activities, saving enormous effort in their data-gathering work and leaving more time for analysis and creativity. |