Related papers: Finding the period of a simple pendulum
We present a self-contained development of Gauss' Arithmetic-Geometric Mean (AGM) and the work of A.E. Ingham who obtained rigorous error bounds for the AGM approximations to the period of a simple pendulum
We describe the correct cubic relation between the mass configuration of a Kater reversible pendulum and its period of oscillation. From an analysis of its solutions we conclude that there could be as many as three distinct mass…
The prepared doctoral dissertation focuses on studying dynamics of systems composed of magnetic pendulums subjected to a non-stationary magnetic field. A magnetic pendulum is a physical pendulum with a magnet attached to its end and is…
In this paper we prove a relation between the period of an elliptic curve and the period of its real and imaginary quadratic twists. This relation is often misstated in the literature.
Experiments on the oscillatory motion of a suspended bar magnet throws light on the damping effects acting on the pendulum. The viscous drag offered by air was found the be the main contributor for slowing the pendulum down. The nature and…
The tautochrone on a cycloid curve is usually considered without drag force. In this work, we investigate the motion of a damped cycloidal pendulum under presence of a drag force. Using the Lagrange formulation, and considering linear…
Two simple, interpolatory-like linearizations are shown for the simple pendulum which can be used for any initial amplitude.
With the right choice of sensor, a `simple' pendulum has great potential as a seismometer with superior low frequency sensitivity.
The purpose of this paper is to show that: when a single particle moving under 3-proper time (three-dimensional time), the trajectories of a classical particle are equivalent to a quantum field with spin. Three-proper time models are built…
We develop a simple method to obtain approximate analytical expressions for the period of a particle moving in a given potential. The method is inspired to the Linear Delta Expansion (LDE) and it is applied to a large class of potentials.…
This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…
A numerical study of the quantum double pendulum is conducted. A suitable quantum scaling is found which allows to have as the only parameters the ratios of the lengths and masses of the two pendula and a (quantum) gravity parameter…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
This study investigates the dynamics of a magnetic pendulum under time-varying magnetic excitation with a position-dependent phase. The system exhibits complex chaotic and regular dynamics, validated through simulations and experiments. The…
We present a pedagogical introduction to Floquet-Magnus theory through the classical example of Kapitza's pendulum - a simple system exhibiting nontrivial dynamical stabilization under rapid periodic driving. By deriving the equations of…
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…
If time is described by a fundamental process rather than a coordinate, it interacts with any physical system that evolves in time. The resulting dynamics is shown here to be consistent provided the fundamental period of the time system is…
In this work we solve the nonlinear second order differential equation of the simple pendulum with a general initial angular displacement ($\theta(0)=\theta_0$) and velocity ($\dot{\theta}(0)=\phi_0$), obtaining a closed-form solution in…
This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some…
We investigate the nonlinear effect of a pendulum with the upper end fixed to an elastic rod which is only allowed to vibrate horizontally. The pendulum will start rotating and trace a delicate stationary pattern when released without…