Damped quadratic and mixed-parity oscillator response using Krylov–Bogoliubov method and energy balance

Approximate analytic solutions of linearly damped quadratic and mixed parity nonlinear oscillators are obtained using the Krylov–Bogoliubov method and considering energy balance during the oscillatory motion. Difference in the system characteristic during the positive and negative half cycles of the oscillations is incorporated by considering two equivalent auxiliary equations of the system. The amplitudes of oscillations during the positive motion and negative motion are obtained using principle of energy balance. Solutions obtained through numerical simulation of the system are compared with the analytic expressions.