  This paper shows that an integrable approximation of the spring pendulum,
when tuned to be in $1:1:2$ resonance, has monodromy. The stepwise precession
angle of the swing plane of the resonant spring pendulum is shown to be a
rotation number of the integrable approximation. Due to the monodromy, this
rotation number is not a globally defined function of the integrals. In fact at
lowest order it is given by $\arg(a+ib)$ where $a$ and $b$ are functions of the
integrals. The resonant swing spring is therefore a system where monodromy has
easily observed physical consequences.
