Damping Cycle Count Three-Row Scan - Oscillations and Coupled Resonance Step by Step

Repeated retention is a countable multiplication before any continuous decay law. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One half-retention cycle leaves four metres

Starting amplitude 8 m is multiplied by one half for cycle count n=1. The retained amplitude is 4 m and the lost amplitude is 4 m.

A_n=8\left({1\over 2}\right)^{1}=4\ \mathrm{m}

Two cycles leave two metres

Starting amplitude 8 m is multiplied by one half for cycle count n=2. The retained amplitude is 2 m and the lost amplitude is 6 m.

A_n=8\left({1\over 2}\right)^{2}=2\ \mathrm{m}

Three cycles leave one metre

Starting amplitude 8 m is multiplied by one half for cycle count n=3. The retained amplitude is 1 m and the lost amplitude is 7 m.

A_n=8\left({1\over 2}\right)^{3}=1\ \mathrm{m}