Related papers: Simple pendulum dynamics: revisiting the Fourier-b…
In this paper, we handle the problem of the motion of the Foucault pendulum. We explore a new method induced from the De Alembert Principle giving the motional equations without small-amplitude oscillation approximation. The result of the…
Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…
The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle…
We present an analysis of the motion of a simple torsion pendulum and we describe how, with straightforward extensions to the usual basic dynamical model, we succeed in explaining some unexpected features we found in our data, like the…
The analytical solution of the three--dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the…
The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…
When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as…
The Fourier-Bessel expansion of a function on a circular disc yields a simple series representation for the end-to-end probability distribution function w(R,phi) encountered in a planar persistent random walk, where the direction taken in a…
A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown…
We explore analytically the quantum dynamics of a point mass pendulum using the Heisenberg equation of motion. Choosing as variables the mean position of the pendulum, a suitably defined generalised variance and a generalised skewness, we…
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 article aims to answer the question, "What is the simplest system that embodies the essence of Foucault's pendulum?" We study a very elementary idealized system that exhibits a precession behavior analogous to the classic pendulum. The…
We study the apsidal precession of a Physical Symmetrical Pendulum (Allais' precession) as a generalization of the precession corresponding to the Ideal Spherical Pendulum (Airy's Precession). Based on the Hamilton-Jacobi formalism and…
The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…
The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in…
The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be…
We present an experimental setup to demonstrate normal modes and symmetry breaking in a two-dimensional pendulum. In our experiment we have used two modes of a single oscillator to demonstrate normal modes, as opposed to two single…
If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often…
We provide an exact infinite power series solution that describes the trajectory of a nonlinear simple pendulum undergoing librating and rotating motion for all time. Although the series coefficients were previously given in [V. Fair\'en,…
Galileo, in the XVII century, observed that the small oscillations of a pendulum seem to have constant period. In fact, the Taylor expansion of the period map of the pendulum is constant up to second order in the initial angular velocity…