Abstract When an external force is applied to the pendulum, it leaves the equilibrium state, and after some transient, starts to oscillate in a steady-state manner. As parameters are varied, the system can undergo a series of bifurcations. One of the simplest forms of instability is the saddle-node bifurcation, which results in a jump phenomenon. This is often a purely deterministic event in which the pendulum jumps to resonance in a predictable manner. We show, however, that if the steady-state solution finds itself on a fractal basin boundary at the point of instability, we cannot predict the dynamics of the jump. We present resonance response diagrams, as the frequency is varied, to illustrate this behaviour.