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…

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…

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…

Despite its frequent use, there is little understanding of the concept of differential
among upper high school and undergraduate students of physics. As a first step to identify the origin of this situation and to revert it, we have done…

This paper deals with the non-linear oscillation of a simple pendulum and presents an approach for solving the non-linear differential equation that governs its movement by using the harmonic balance method. With this technique it is possible to easily obtain…

We examine the evolution of the refractive index modulation when recording gratings in an acrylamide based photopolymer. A nonlocal diffusion model is used to predict theoretically the grating evolution. The model has been developed to account for both nonlocal spatial…

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…

In this work we study the effect of the glass substrate on the efficiencies of the different orders that propagate inside a transmission sinusoidal diffraction grating. Holographic optical elements are usually recorded on a photosensitive medium deposited on to a…

The analytical approximate technique developed by Wu et al. for conservative oscillators with odd nonlinearity is used to construct approximate frequency-amplitude relations and periodic solutions to the relativistic oscillator. By combining Newton's method with the method of harmonic balance, analytical…

A more accurate analytical approximate expression for the slope at any point of the elastic curve of a slender cantilever column is obtained by using a heuristic but pedagogical derivation. This derivation is based on the linearization of the nonlinear…