Matching Drive Kicks Add Coherently - Oscillations and Coupled Resonance Step by Step

The toy drive ledger accepts growth only at matching frequency. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Matching frequency opens the coherent ledger

The drive frequency and natural frequency are both 4 hertz, so the match label is yes.

f_\mathrm{drive}=f_\mathrm{nat}=4\ \mathrm{Hz}

Four accepted kicks add to eight joules

Four kicks of 2 joules each give accepted growth 8 joules.

4\cdot 2=8\ \mathrm{J}