Homotopy perturbation method for Fangzhu oscillator

An accurate frequency-amplitude relationship is very needed to elucidate the properties of the oldest device of Fangzhu for collecting water from the air. The Fangzhu oscillator was derived and solved approximately (He et al. in Math Methods Appl Sci, 2020, 10.1002/mma.6384), here we show that the singular Duffing-like oscillator can be more effectively solved by the homotopy perturbation method and a criterion is obtained for the existence of a periodic solution for the singular differential equation. The results obtained in this paper are helpful for the optimal design of the Fangzhu device.