A pendulum in a superfluid Imagine to submerge a pendulum in a supefluid. Of course we assume an ideal pendulum, whose joint does not freeze or deteriorate due to the extremely low temperature. We also assume the superfluid to be at zero temperature, so we can neglect its normal component.
What happens to its oscillations? Are they somehow damped? Or do they keep a constant amplitude?
In other words: can some energy be transferred from the pendulum to the superfluid (for example, thanks to the excitation of sound waves in the superfluid)?
 A: If the pendulum is fully submerged (and the velocity of the sphere is sufficiently small) then the flow around the sphere is Stokes flow, and the drag is proportional to viscosity. As a result there is no drag in a zero temperature superfluid. If the sphere is only partially submerged, then it can excite surface waves which take away energy. This setup is not completely academic — torsion pendulums have been used to measure the viscosity of liquid helium.
Further remarks:

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*The drag is described by Stokes formula $F=6\pi \eta RV$, where $\eta$ is the viscosity of the normal fluid, $R$ is the radius of the sphere, and $v$ is the velocity relative to the fluid. Drag vanishes if $\eta$ vanishes, or the normal density vanishes.


*If the sphere is only partially submerged then there is a free surface and Stokes solution does not apply. Indeed, more generally, d'Alembert's paradox does not apply. An object will generate a bow wave in an inviscid fluid, and this leads to drag.


*Every superfluid has a critical velocity. If the velocity of the object exceeds that velocity, then superfluidity breaks down, even at very small temperature.
