Related papers: Finding the period of a simple pendulum
A modulated oscillation in two or three dimensions can be represented as the trajectory traced out in space by a particle orbiting an ellipse, the properties of which vary as a function of time. Generalizing ideas from signal analysis, the…
The pedal of a curve in the Euclidean plane is a classical subject which has a singular point at the inflection point of the original curve or the pedal point. The primitive of a curve is a curve given by the inverse construction for making…
In this paper we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian System of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables perturbation. The…
The Randall-Sundrum models are expected to modify the short distance behavior of general relativity. In this paper, we will propose an experimental test for this short distance modification due to Randall-Sundrum models. This will be done…
We consider the rotational dynamics in an ensemble of globally coupled identical pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of…
Some of the principal heliophysical inferences that have been drawn from, or refined by, seismology, and the manner in which those inferences have been made, are very briefly described. Prominence is given to the use of simple formulae,…
In the context of physics didactics, alternative instructional approaches have often been employed to facilitate conceptual understanding of various topics. In this article, an alternative formulation for analyzing the motion of bodies on…
The search for electric dipole moments of particles in storage rings requires the development of dedicated deflector elements with electrostatic fields. In these rings, electric deflectors shall be used as bending elements for the charged…
We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…
We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…
Here we show that the concepts behind such terms as entanglement, qubits, quantum gates, quantum error corrections, unitary time evolution etc., which are usually ascribed to quantum systems, can be adequately realized on a set of coupled…
An experiment is proposed which can distinguish between two approaches to the reality of the electric field, and whether it has mechanical properties such as mass and stress. A charged pendulum swings within the field of a much larger…
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
The interval approach to computation of dynamics of celestial bodies in the planetary problem has been considered. It is based on the refusal from idealization of infinitely high resolving capacity of measuring tools, and forms an…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…
Many damped mechanical systems oscillate with increasing frequency as the amplitude decreases. One popular example is Euler's Disk, where the point of contact rotates with increasing rapidity as the energy is dissipated. We study a simple…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
We provide sufficient conditions for the existence of periodic solutions of the planar perturbed double pendulum with small oscillations.
We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive…
We establish an instructive experiment to investigate the minimum time curve traveled by a small billiard ball rolling in a grooved track under gravity. Our intention is to popularize the concept of \textit{minimum time curve} anew, and to…