An uninitiated student would expect the motion might be simple harmonic. And for very small initial displacement, as shown in the photo at left, the motion is repetitive, insensitive to initial conditions and Newtonian deterministic. But when given a large intitial displacement, as shown in the photo at right, the nature of the motion changes dramatically. It shows chaotic motion. It does not repeat and it is very sensitive to the initial conditions.
Newtonian analysis is deficient to predict it.
The chaotic treatment looks at the phase space of the system to find the space-filling orbitals and the attractors. When the students see this demo for the first time there is a tremendous response. The WOW factor is a 10 and it is considered a favorite demonstration of the semester in any course. On the last day of class students may ask to see it one more time. Chaotic pendulum, as photographed.