Oscillation Relation Cross Scans

Drive Match Three-Row Scan

The finite kick ledger accepts growth only when the drive frequency matches. 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 accepts all four kicks

The natural frequency is 4 Hz and the drive frequency is 4 Hz. Match is yes, so accepted growth is 8 J.

fdrive=4 Hz=4 Hz⇒G=8 Jf_\mathrm{drive}=4\ \mathrm{Hz}=4\ \mathrm{Hz}\Rightarrow G=8\ \mathrm{J}
Drive match scanFrequency match and accepted growth are checked.f0=4 Hzfdrive=4 HzkickTotal=8 Jaccepted=8 Jmatch=yeskick1=2 Jkick2=2 Jkick3=2 Jkick4=2 J

A lower drive frequency rejects coherent growth

The natural frequency is 4 Hz and the drive frequency is 3 Hz. Match is no, so accepted growth is 0 J.

fdrive=3 Hz≠4 Hz⇒G=0 Jf_\mathrm{drive}=3\ \mathrm{Hz}\ne4\ \mathrm{Hz}\Rightarrow G=0\ \mathrm{J}
Drive match scanFrequency match and accepted growth are checked.f0=4 Hzfdrive=3 HzkickTotal=8 Jaccepted=0 Jmatch=nokick1=2 Jkick2=2 Jkick3=2 Jkick4=2 J

A further mismatch still accepts zero growth

The natural frequency is 4 Hz and the drive frequency is 2 Hz. Match is no, so accepted growth is 0 J.

fdrive=2 Hz≠4 Hz⇒G=0 Jf_\mathrm{drive}=2\ \mathrm{Hz}\ne4\ \mathrm{Hz}\Rightarrow G=0\ \mathrm{J}
Drive match scanFrequency match and accepted growth are checked.f0=4 Hzfdrive=2 HzkickTotal=8 Jaccepted=0 Jmatch=nokick1=2 Jkick2=2 Jkick3=2 Jkick4=2 J