Related papers: Oscillations bounded by the simple pendulum and th…
The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated…
Sustained oscillations in power systems are dangerous. There are various mechanisms, for instance, limit cycle and forced oscillation, that may lead to sustained oscillations, which nevertheless are hard to differentiate. In this paper, a…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
The characteristics of drive-free oscillations of a damped simple pendulum under sinusoidal potential force field differ from those of the damped harmonic oscillations. The frequency of oscillation of a large amplitude simple pendulum…
We develop an analytic formalism and derive new exact relations that express the short-time dispersion of fluid particles via the single-time velocity correlation functions in homogeneous isotropic and incompressible turbulence. The…
Oscillons, extremely long-living localized oscillations of a scalar field, are studied in theories with quartic and sine-Gordon potentials in two spatial dimensions. We present qualitative results concentrating largely on a study in…
This paper considers a nonlinear spherical pendulum whose suspension point performs high-frequency spatial vibrations. The dynamics of this pendulum can be described by averaging its Hamiltonian over phases of vibrations. Rotationally…
A compound pendulum of simple geometry was built from a lightweight rod to which a pair of masses are clamped, one above and the other below the axis of rotation. By making the position of the upper mass variable, it was found that the…
To investigate the rigidity and flexibility of Lagrangian cobordisms between Legendrian submanifolds, we investigate the minimal length of such a cobordism, which is a $1$-dimensional measurement of the non-cylindrical portion of the…
Simple physical models of a measuring rod and of a clock are used to demonstrate the contraction of objects and clock retardation in special relativity. It is argued that the models could help in promoting student understanding of special…
We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating…
Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…
The humble pendulum is often invoked as the archetype of a simple, gravity driven, oscillator. Under ideal circumstances, the oscillation frequency of the pendulum is independent of its mass and swing amplitude. However, in most real-world…
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…
We theoretically study the dynamics of a pair of coupled pendulums subject to a periodic temporal modulation of their oscillation frequency. Inspired from analogous developments in quantum mechanics, we anticipate dynamical localization and…
In this letter we study the classical motion of an electric dipole in the presence of a uniform magnetic field in the approximation of small oscillations. The normal modes of oscillations are obtained and propose a criterion of…
The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
We study when a physical operation can produce entanglement between two systems initially disentangled. The formalism we develop allows to show that one can perform certain non-local operations with unit probability by performing local…
The Wilberforce pendulum is a great experience for illustrating important properties of coupled oscillatory systems, such as normal modes and beat phenomena, in physics courses. A helical spring attached to a mass comprises this simple but…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…