Coupled Resonators Have Normal Modes

Oscillation Audit Cites Every Source

The capstone audit joins phase, energy, drive, damping, and modes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two displacements decompose into two mode coordinates

Displacements 6 metres and 2 metres give q plus 4 metres and q minus 2 metres.

q+=6+22=4,q−=6+(−2)2=2q_+={6+2\over 2}=4,\quad q_-={6+(-2)\over 2}=2
Mode-coordinate sourceThe superposition check reconstructs the original displacements.x1=6 mx2=2 mq_plus=4 mq_minus=2 mre_x1=6 mre_x2=2 m

The audit cites every checked source

The final accepted bit is 1 because phase, energy, drive, damping, coupled mode, and superposition sources all match.

audit=1\mathrm{audit}=1
Oscillation auditEach cited final value comes from a checked source.accepted=1