In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the Green function. In this paper we obtain the same result with an alternative proof via known issues of classical averaging theory. This theory provides a useful means to study a planar differential equation derived from the pendulum clock, accessible to Master and PhD students. (Contains 1 figure.)