Simple pendulum revisited

Aggarwal, Neha; Verma, Nitin; Arun, P.

doi:10.1088/0143-0807/26/3/016

Cited by 22 publications

(22 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…If we demand an acceptable error of 0.5%, we find that the acceptable small-angle boundary would be 0.211 rad or 12 • . This boundary for the small-angle regime is in good agreement with earlier reports [24]. Interestingly, if we revisit Eq.…”

Section: Fourier Series Analysis Of the Nonlinear Pendulum Motionsupporting

confidence: 93%

“…In the case of SHM, for the initial condition θ(t = 0) = θ m andθ(t = 0) = 0, one can expect a 1 = θ m and b 1 = 0, thus enabling us to identify the small-angle condition. This method is unique when compared to those found in literature [24]. In order to study the mentioned transition, we have solved Eq.…”

Section: Fourier Series Analysis Of the Nonlinear Pendulum Motionmentioning

confidence: 99%

See 1 more Smart Citation

Fourier analysis of nonlinear pendulum oscillations

Singh¹,

Arun²,

Lima

2018

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

Since the times of Galileo, it is well-known that a simple pendulum oscillates harmonically for any sufficiently small angular amplitude. Beyond this regime and in absence of dissipative forces, the pendulum period increases with amplitude and then it becomes a nonlinear system. Here in this work, we make use of Fourier series to investigate the transition from linear to nonlinear oscillations, which is done by comparing the Fourier coefficient of the fundamental mode (i.e., that for the small-angle regime) to those corresponding to higher frequencies, for angular amplitudes up to 90 •. Contrarily to some previous works, our results reveal that the pendulum oscillations are not highly anharmonic for all angular amplitudes. This kind of analysis for the pendulum motion is of great pedagogical interest for both theoretical and experimental classes on this theme.

show abstract

Section: Fourier Series Analysis Of the Nonlinear Pendulum Motionsupporting

confidence: 93%

Section: Fourier Series Analysis Of the Nonlinear Pendulum Motionmentioning

confidence: 99%

Fourier analysis of nonlinear pendulum oscillations

Singh¹,

Arun²,

Lima

2018

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

show abstract

“…This phase difference is caused by a very small difference in frequency between the nonlinear models and the linear model, which adds up over many cycles. The small lag gets larger if the initial displacement from the equilibrium is made larger [18]. Fig.…”

Section: Dynamic System Responsementioning

confidence: 95%

Stability of gas pressure regulators

Zafer

Luecke

2008

Applied Mathematical Modelling

View full text Add to dashboard Cite

Gas pressure regulators are widely used in both commercial and residential applications to control the operational pressure of the gas. One common problem in these systems is the tendency for the regulating apparatus to vibrate in an unstable manner during operation. These vibrations tend to cause an auditory hum in the unit, which may cause fatigue damage and failure if left unchecked. This work investigates the stability characteristics of a specific type of hardware and shows the cause of the vibration and possible design modifications that eliminate the unstable vibration modes. A dynamic model of a typical pressure regulator is developed, and a linearized model is then used to investigate the sensitivity of the most important governing parameters. The values of the design parameters are optimized using root locus techniques, and the design trade-offs are discussed.

show abstract

“…More than a decade ago, the WA98 Collaboration has measured the elliptic flow v 2 of photons produced in P b + P b collisions at the beam energy of E beam = 158 AGeV [203], and it was found that the v 2 (γ incl ) of the low-transverse-momentum inclusive photons was about equal to the v 2 (π) of pions within the experimental uncertainties. This observation lead to the conclusion that either (Scenario a:) the contribution of the direct photons to the inclusive ones is negligible in comparison to the decay photons, i.e.…”

Section: Elliptic Flow Of Direct Photonsmentioning

confidence: 95%

Effective QCD and transport description of dilepton and photon production in heavy-ion collisions and elementary processes

Linnyk

Bratkovskaya

Cassing

2016

Progress in Particle and Nuclear Physics

145

108

View full text Add to dashboard Cite

In this review we address the dynamics of relativistic heavy-ion reactions and in particular the information obtained from electromagnetic probes that stem from the partonic and hadronic phases. The out-of-equilibrium description of strongly interacting relativistic fields is based on the theory of Kadanoff and Baym. For the modeling of the partonic phase we introduce an effective dynamical quasiparticle model (DQPM) for QCD in equilibrium. In the DQPM, the widths and masses of the dynamical quasiparticles are controlled by transport coefficients that can be compared to the corresponding quantities from lattice QCD. The resulting off-shell transport approach is denoted by Parton-Hadron-String Dynamics (PHSD) which includes covariant dynamical transition rates for hadronization and keeps track of the hadronic interactions in the final phase. It is shown that the PHSD captures the bulk dynamics of heavy-ion collisions from lower SPS to LHC energies and thus provides a solid basis for the evaluation of the electromagnetic emissivity on the basis of the same dynamical parton propagators that are employed for the dynamical evolution of the partonic system. The production of direct photons in elementary processes and heavy-ion reactions is discussed and the present status of the photon v 2 "puzzle" -a large elliptic flow v 2 of the direct photons experimentally observed in heavy-ion collisions -is addressed for nucleus-nucleus reactions at RHIC and LHC energies. The role of hadronic and partonic sources for the photon spectra and the flow coefficients v 2 and v 3 are considered as well as the possibility to subtract the QGP signal from the experimental observables. Furthermore, the production of e + e − or µ + µ − pairs in elementary processes and A+A reactions is addressed. The calculations within the PHSD from SIS to LHC energies show an increase of the low mass dilepton yield essentially due to the in-medium modification of the ρ-meson and at the lowest energy also due to a multiple regeneration of ∆-resonances. Furthermore, pronounced traces of the partonic degrees-of-freedom are found in the intermediate dilepton mass regime (1.2 GeV < M < 3 GeV) at relativistic energies, which will also shed light on the nature of the very early degrees-of-freedom in nucleus-nucleus collisions.

show abstract

Simple pendulum revisited

Cited by 22 publications

References 5 publications

Fourier analysis of nonlinear pendulum oscillations

Fourier analysis of nonlinear pendulum oscillations

Stability of gas pressure regulators

Effective QCD and transport description of dilepton and photon production in heavy-ion collisions and elementary processes

Contact Info

Product

Resources

About