A convenient technique for evaluating angular frequency in some nonlinear oscillations

In this paper, a convenient technique for evaluating angular frequency in some nonlinear oscillations is proposed. It is well known that once the restoring force function is given beforehand, the period of motion can be determined by an integral. The angular frequency has a relation with the period of motion as well as the integral. One makes a little modification for the integrand in the integral and a change of variable. It is found that if the three divisions are chosen on the integration interval and the trapezoid quadrature rule is used, a higher accurate result for the angular frequency can be achieved. For the restoring force being an odd function, three numerical examples are presented. The eardrum-type oscillation is studied as well. Higher accurate results for the angular frequency are obtained in all those examples.