Can Oscillations of a Simple Pendulum Explain the Oscillations of a Fluid Interface?

Understanding the phenomena of resonance in fluid systems is important due to its relevance in heat removal applications in microgravity environments in space. In this work, we utilize the effect of resonance on the oscillations of a simple pendulum to elucidate the interface behavior of a fluid layer subjected to vertical oscillations. A simple pendulum suspended from a base plate will oscillate at its natural frequency when slightly disturbed. If the pendulum bob is heavy, the damping of these oscillations due to the air resistance will be negligible, and the natural frequency will depend only on the gravitational acceleration and the inverse of the pendulum length. When the base plate of the pendulum is vertically oscillated near its natural frequency, the pendulum bob will oscillate violently due to resonance. Analogously, fluid systems also have a natural frequency, and the interface of the fluid layer will exhibit large undulations or patterns when vertically oscillated near its natural frequency. The natural frequency of a fluid layer in the absence of viscous damping depends on the gravitational acceleration, surface tension and the wavelength of the pattern observed at the interface. To this end, we demonstrate the effect of resonance on different pendulum lengths and use it to explain the emergence of various patterns with different wavelengths at the interface of a fluid layer undergoing vertical oscillations.