Related papers: Dynamics and performance of clock pendulums
Some recent results on the rotational dynamics of polymers are reviewed and extended. We focus here on the relaxation of a polymer, either flexible or semiflexible, initially wrapped around a rigid rod. We also study the steady polymer…
We formulate a phenomenological model to study the power applied by a cyclist on a velodrome\, -- \,for individual timetrials\, -- \,taking into account the straights, circular arcs, connecting transition curves and banking. The dissipative…
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…
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 consider dissipative one-dimensional systems subject to a periodic force and study numerically how a time-varying friction affects the dynamics. As a model system, particularly suited for numerical analysis, we investigate the driven…
If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs:…
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…
Using a combination of theory, experiment, and simulation, we revisit the dynamics of two coupled metronomes on a moving platform. Our experiments show that the platform's motion is damped by a dry friction force of Coulomb type, not the…
In Part I of this paper series, a theoretical and numerical model for a a driven pendulum filled with liquid was developed. The system was analyzed in the framework of tuned liquid dampers (TLD) and hybrid mass liquid dampers (HMLD) theory.…
A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have…
Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there…
The recent experimental realization of a three-dimensional (3D) optical lattice clock not only reduces the influence of collisional interactions on the clock's accuracy but also provides a promising platform for studying dipolar many-body…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
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…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
A physical pendulum with variable point of suspension (and, as an outcome, variable inertia moment) is experimentally analysed. In particular, the period of the small oscillations as a function of position of the suspension point is…
We study the dynamics of MEMS microbeams undergoing electrostatic pull-in. At DC voltages close to the pull-in voltage, experiments and numerical simulations have reported `bottleneck' behaviour in which the transient dynamics slow down…
In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating…
In this note we discuss the usage of the Dirac $\delta$ function in models of phase oscillators with pulsatile inputs. Many authors use a product of the delta function and the phase response curve in the right hand side of an ODE to…
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…