Summary: The motion of a cylindrical torsion pendulum, which is immersed in a viscous liquid, is described by a system of differential equations, which is solved in closed form. If the diffusion length of the vorticity is much larger than the width of the gap between the pendulum and the container, the classical quasi-stationary solution is a good approximation of the exact solution. If the diffusion length is small, the flow is non-stationary and the quasi-stationary solution is not valid. If the pendulum is immersed in an infinite container, there is no critical damping in the ordinary sense.