T = 2π√(L/g) (small-angle pendulum)
Energy: E = ½mv² + mgh − damping loss
A diagnostic rig runs known reference systems — a pendulum, a bouncing ball, a spring — under controlled gravity, damping and restitution, then compares the measured behaviour against closed-form theory. Large discrepancies flag numerical-integration or constant errors before the engine is trusted for complex simulations.
- Gravity g — sets the acceleration for all three test rigs simultaneously.
- Damping — velocity-proportional energy loss applied to pendulum and spring oscillation.
- Restitution — bounce energy retention fraction for the falling ball test.
- Run Calibration Test — times one full pendulum swing and compares it to the theoretical T = 2π√(L/g).
Real-world use: exactly this kind of baseline diagnostic (known pendulum length, timed period, compared to theory) is how physics engines, lab instruments, and even smartphone accelerometers are calibrated before trusted for real measurements.