Related papers: Thinking Hard About Physics Before Calculating: An…
A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be…
The stability of standing in humans is a complex process that leads to maintaining the upright position against external disturbances. Balance control during standing is of vital importance for humans in daily life. An issue that is still…
The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $\beta$…
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…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
The normal and the inverted pendulum continue to be one of the main physical models and metaphors in science. The inverted pendulum is also a classic study case in control theory. In this paper we consider a special demonstration version of…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
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 presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions.…
Quantum entanglement is a captivating phenomenon in quantum physics, characterized by intricate and non-classical correlations between particles. This phenomenon plays a crucial role in quantum computing and measurement processes. In this…
The purpose of this paper is to present an introduction to a point of view for discrete foundations of physics. In taking a discrete stance, we find that the initial expression of physical theory must occur in a context of noncommutative…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
An "upward-driven disk" is a novel mechanical device built from LEGO parts. A circular disk is suspended from the point where it is sandwiched between two wheels, making it free to oscillate as a pendulum, but the location of that…
Recently researchers at the University of Illinois coupled a real pendulum to its virtual counterpart. They observed that the two pendulums suddenly start to move in synchrony if their lengths are sufficiently close. In this synchronized…
In the usual rod and slot paradox, the rod, if it falls, was expected to fall into the slot due to gravity. Many thought experiments have been conducted where the presence of gravity is eliminated with the rod and slot approaching each…
We study period doublings in $N$ $(N=2,3,4, \dots)$ coupled parametrically forced damped pendulums by varying $A$ (the amplitude of the external driving force) and $c$ (the strength of coupling). With increasing $A$, the stationary point…
In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top…
A unified, consistent and simple view of the Faraday law of induction is presented, which consists of two points: discriminating the lab- from the rest-frame electric field and understanding it is the impossibility for both fields to vanish…
Several scenarios used in teaching feature a rolling motion with slipping that transitions to one without through friction with the ground. We summarise these transitions by introducing an unknown impulse that is transferred to the ground.…
The French Academy units of time and length - the second and the meter - are traditionally considered independent from each other. However, it is a matter of fact that a meter simple pendulum beats virtually the second in each oscillation,…