AN ANALYTICAL TECHNIQUE TO OBTAIN HIGHER-ORDER APPROXIMATE PERIODS FOR THE NONLINEAR OSCILLATOR

In this paper, an analytical technique has been proposed to obtain higher-order approximate periods for the nonlinear oscillator with the square of the angular frequency depending quadratically on the velocity which is based on the harmonic balance method (HBM). Analytical investigation of the appeared set of nonlinear algebraic equations is usually cumbersome, which is addressed by the proposed technique in a novel way. In this paper, this limitation is eradicated and provides desired results without much numerical complexity. Additionally, a new suitable truncation formula has been introduced in which the approximate periods measure much better results than existing periods. The proposed technique is applied to the benchmark nonlinear oscillatory problem where the square of the angular frequency depends quadratically on the velocity to illustrate its novelty, reliability, and wider applicability. It is remarkably improtant to note that, using the proposed technique, a third-order approximate period gives an excellent agreement as compared with the exact ones.