Related papers: Finding the period of a simple pendulum
We consider a simple pendulum whose suspension point undergoes fast vibrations in the plane of motion of the pendulum. The averaged over the fast vibrations system is a Hamiltonian system with one degree of freedom depending on two…
In this work, the relativistic phenomena of Lorentz contraction and time dilation are derived using a modified distance formula appropriate for discrete space. This new distance formula is different than Pythagoras's theorem but converges…
What is the major difference between large and small systems? At small length-scales the dynamics is dominated by fluctuations, whereas at large scales fluctuations are irrelevant. Therefore, any thermodynamically consistent description of…
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…
The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
Models of period variations are basic tools for period analyzes of variable stars. We introduce phase function and instant period and formulate basic relations and equations among them. Some simple period models are also presented.
The study of classical waves in time-periodic systems is experiencing a resurgence of interest, motivated by their rich physics and the new engineering opportunities they enable, with several analogies to parallel efforts in other branches…
A generalization of the classical Kapitza pendulum is considered: an inverted planar mathematical pendulum with a vertically vibrating pivot point in a time-periodic horizontal force field. We study the existence of forced oscillations in…
Time series of string tension of a simple pendulum has not yet been a interesting motion information, even nowadays using a force tension sensor can be measured easily. A numerical procedure is presented how to obtain motion of pendulum bob…
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…
Longitudinal oscillations in prominences are common phenomena on the Sun. These oscillations can be used to infer the geometry and intensity of the filament magnetic field. Previous theoretical studies of longitudinal oscillations made two…
We establish a relationship between the normalized damping coefficients and the time that takes a nonlinear pendulum to complete one oscillation starting from an initial position with vanishing velocity. We establish some conditions on the…
Galileo noted in the 16th century that the period of oscillation of a pendulum is almost independent of the amplitude. However, such a pendulum is damped by air friction. The latter may be viewed as resulting from air molecules getting in…
We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
A driven pendulum with vertical oscillations of pendulum support (Kapitza pendulum) possesses a number of unusual properties and is a popular object of both analytical and numerical studies. Although some spectacular results can be…
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the…
The inverted pendulum is a mechanical system with a rapidly oscillating pivot point. Using techniques similar in spirit to the methodology of effective field theories, we derive an effective Lagrangian that allows for the systematic…
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…
Pulsars are good clocks in the universe. One fundamental question is that why they are good clocks? This is related to the braking mechanism of pulsars. Nowadays pulsar timing is done with unprecedented accuracy. More pulsars have braking…