Related papers: An analog simulation experiment to study free osci…
Models of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of torques applied to keep the swing moving in…
In this work, the force due to radiation pressure is measured with sub-10 pN sensitivity, corresponding to less than 2 mW of optical power. The apparatus adds homemade reflectors to a commercial Cavendish balance, which consists of a…
We run molecular dynamics simulations of folded graphene sheets and present a procedure to measure the sliding friction in these systems based on the rate of decay of a damped-harmonic oscillator. This procedure allowed us to study the…
The oscillation periods bounded by a simple pendulum and an oscillating rigid rod are illustrated using a multiple pendulum. Oscillation periods between these two limits are obtained. A theoretical approach using the Lagrangian formalism…
A liquid meniscus, a bending rod (also called elastica) and a simple pendulum are all described by the same non-dimensional equation. The oscillatory regime of the pendulum corresponds to buckling rods and pendant drops, and the…
The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure…
The resonances associated with a fractional damped oscillator which is driven by an oscillatory external force are studied. It is shown that such resonances can be manipulated by tuning up either the coefficient of the fractional damping or…
We want to introduce an atomic pendulum whose driving force (torque) is due to the quantum vacuum fluctuations. Applying the well-known Casimir-Polder effect to a special configuration (a combined structure of an atomic nanostring and a…
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…
We examine the conditions for appearance of symmetry breaking bifurcation in damped and periodically driven pendulum in the case of strong damping. We show that symmetry breaking, unlike other nonlinear phenomena, can exist at high…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
This study investigates the performance of cascade PID control architecture applied to an inverted pendulum on a cart system through both simulation and experimental implementation. A nonlinear model of the system was developed using…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…
A model for harmonic oscillator damping due to the internal friction of solids has been developed, based on considerations of a long period pendulum. The assumption of a complex elastic modulus to describe stress-strain hysteresis in the…
In recent years, science simulations have become popular among educators due to their educational usefulness, availability, and potential for increasing the students' knowledge on scientific topics. In this paper, we introduce the…
This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly…
We study dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the…
A proof-of-principle electron electric dipole moment (e-EDM) experiment using slow cesium atoms, nulled magnetic fields, and electric field quantization has been performed. With the ambient magnetic fields seen by the atoms reduced to less…
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which…