Practice question · Multiple choice
You simulate a pendulum and plot angle vs. time, the curve looks like a clean cosine, but its amplitude slowly grows each swing. Energy should be conserved. What did the plot most likely just catch?
Hints
- The physics says amplitude must stay constant (no driving, no damping). So the discrepancy lives in the numerics.
- Naïve Euler integration systematically overshoots on curved trajectories, adding a little energy every step.
Show the answer
C. Numerical error pumping energy into the system
Why
The plot is a conservation-law audit: growing amplitude reveals the integrator (likely explicit Euler) injecting energy. This is why physicists plot conserved quantities as sanity checks, and why orbital simulations use symplectic integrators that respect energy by construction.
Practise Visualising scientific computation
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