Oscillation Relation Cross Scans

Drive Match Three-Row Scan

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

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