Solution of a quadratic nonlinear oscillator by the method of harmonic balance

This paper deals with the quadratic nonlinear oscillator (QNO) x ¨ + x + ε x 2 = 0 . This oscillator is compared with the nonlinear oscillators x ¨ + x ± ε | x | x = 0 , which are solved by the method of harmonic balance. Therefore, we obtain the first approximate solution to the QNO. This solution is more accurate than the second approximate solution obtained by the Lindstedt–Poincaré method. For QNOs, it has been pointed out that the angular frequency for x ⩾ 0 should be different from the angular frequency for x ⩽ 0 if solutions of higher degree of accuracy are required.