Oscillation properties of a simple pendulum in a viscous liquid

This paper studies the oscillation properties of a simple pendulum immersed in a viscous liquid. A nonlinear equation of motion for the pendulum is first established by considering both viscous damping and quadratic damping, and solved by using the improved averaging method. Then a relationship between the oscillation period and the viscosity of liquid is derived. The experimental data obtained are consistent with the theoretical prediction, which also suggests a new approach to measure the liquid viscosity. We believe that this paper may be helpful for broadening teaching content for the simple pendulum and for better understanding the vibration of an object in liquids in some applications.