Abstract

In the paper, HE’s energy balance method and HE’s Hamiltonian approach are used to derive simple approximate formulas for the dependence of the frequency of a pendulum-like nonlinear oscillator on its amplitude. Such kind of oscillators are frequently encountered in many fields of engineering and three examples from mechanical domain are given and utilized in the numerical simulations. By comparison with the exact solution, it is shown that obtained formulas lead to high accuracy for initial amplitudes lower than 900 (when the relative errors do not exceed 0.2%) and acceptable closeness for amplitudes well beyond the small-angle regime (here the relative errors are about 5-6% for amplitudes as high as 1500). Results furnished by energy balance method and Hamiltonian approach are contrasted with those provided by other techniques which generally need much more sophisticated procedures