Jose J. Rodes

Approximation for a large-angle simple pendulum period

An approximation scheme to obtain the period for large amplitude oscillations of a simple pendulum is analysed and discussed. The analytical approximate formula for the period is the same as that suggested by Hite (2005 Phys. Teach. 43 290), but it is now obtained analytically by means of a term-by-term comparison of the power-series expansion for the approximate period with the corresponding series for the exact period.

An analysis of the classical Doppler effect

The Doppler effect is a phenomenon which relates the frequency of the harmonic waves generated by a moving source with the frequency measured by an observer moving with a different velocity from that of the source. The classical Doppler effect has usually been taught by using a diagram of moving spheres (surfaces with constant phase) centred at the source. This method permits an easy and graphical interpretation of the physics involved for the case in which the source moves with a constant velocity and the observer is at rest, or the reciprocal problem (the source is at rest and the observer moves). Nevertheless it is more difficult to demonstrate, by this method, the relation of the frequencies for a moving source and observer. We present an easy treatment where the Doppler formulae are obtained in a simple way. Different particular cases will be discussed by using this treatment.

Relation between surface curvature and electrostatic potential of a long charged isolated conductor

In this paper, we analyze the relation between the surface curvature of an isolated charged conductor and resultant electrostatic potential. The study will be performed for a long conductor with uniform cross section. It will be demonstrated by geometric arguments that a correlation between curvature and potential exists. This relation will be obtained for a set of polar coordinates that parameterize the surface of the isolated conductor. Two examples will be discussed based on quasi-circular conducting cylinders, whose cross sections are obtained firstly perturbing the equation of the circle by a cosine function and secondly by a more general function including a Fourier series expansion.

On the physical meaning of the 2.1 keV absorption feature in 4U 1538 52

The improvement of the capabilities of nowadays X-ray observatories, like Chandra or XMM-Newton, offers the possibility to detect both absorption and emission lines and to study the nature of the matter surrounding the neutron star in X-ray binaries and the phenomena that produce these lines. The aim of this work is to discuss the different physical scenarios in order to explain the meaning of the significant absorption feature present in the X-ray spectrum of 4U 1538-52. Using the last available calibrations, we discard the possibility that this feature is due to calibration, gain effects or be produced by the X-ray background or a dust region. Giving the energy resolution of the XMM-Newton telescope we could not establish if the line is formed in the atmosphere of the neutron star or by the dispersion of the stellar wind of the optical counterpart.

Reply to 'Comment on "Approximation for the large-angle simple pendulum period"'

In their comment, Yuan and Ding derived another analytical approximate expression for the large-angle pendulum period, which they compare with other expressions previously published. Most of these approximate formulas are based on the approximation of the original nonlinear differential equation for the simple pendulum motion. However, we point out that another procedure is possible to obtain an approximate expression for the period. This procedure is based on the approximation of the exact period formula—which is expressed in terms of a complete elliptic integral of the first kind—instead of the approximation of the original differential equation. This last procedure is used, for example, by Carvalhaes and Suppes using the arithmetic–geometric mean.

Three approaches to calculating the velocity profile of a laminar incompressible fluid flow in a hollow tube

We present three ways of treating the problem of fluid flow in a hollow cylinder. One method involves a differential equation, and the other two involve more physical insight. We discuss the relative advantages of each method.