The harmonic balance method is used to construct approximate frequency–amplitude relations and periodic solutions to the relativistic oscillator. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic…

We analyse the effects on the stopping power due to the geometrical structure of swift Bn+ (n = 2-6) ions incident on amorphous carbon targets. We use the dielectric formalism to describe both the interaction of the projectile with the…

A new analytical approximate expression for the period of the simple pendulum is obtained by using a heuristic but pedagogical derivation. This formula depends on two parameters obtained by comparing term-by-term the power-series expansions of the approximate and exact expressions…

The electronic energy loss of swift H and He ions in gold is studied, paying special attention to the contribution to the projectile energy loss due to the ionization of the target inner-shells. We calculate the stopping power and the…

We present UBV photometry of the highly reddened and poorly studied open cluster Berkeley 55, revealing an important population of B-type stars and several evolved stars of high luminosity. Intermediate-resolution far-red spectra of several candidate members confirm the presence of…

We present an analysis of a pointed 141 ks Chandra high-resolution transmission gratings observation of the Be X-ray emitting star HD110432, a prominent member of the γ Cas analogs. This observation represents the first high-resolution spectrum taken for this source…

The asymptotic behaviours for small and large amplitudes, A, of the period for a nonlinear oscillator, where the square of the angular frequency depends quadratically on the velocity, are obtained. These asymptotic expressions are compared with the exact period, T(A),…

Two Lidstedt-Poincaré perturbation based methods are used to solve the nonlinear differential equation of a nonlinear oscillator having the square of the angular frequency depends quadratically on the velocity. Mickens published two interesting papers [1, 2] about this oscillator and…

The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency–amplitude relations for a conservative nonlinear oscillatory system in which the restoring force has an irrational form. This system corresponds to the motion of…

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions…