Real numerical simulations you can nudge and watch respond — a spring-mass system across every damping regime, pendulums from predictable to chaotic, and a block sliding down an incline exactly as friction says it should.
A second-order system across all four damping regimes — set the mass, spring and damping, and watch the step response ring, settle, or crawl.
The same Lagrangian mechanics, one, two, or three links deep — from a clean predictable swing to full chaotic motion.
A block on a slope, simulated with real friction — set the angle and coefficients and watch whether it holds, slides, or slides back.