Matching Drive Kicks Add Coherently - Waves, Oscillations, and Resonance Step by Step

The toy drive ledger accepts growth only at matching frequency.

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}