Drive and Damping Are Finite Ledgers

Off-Frequency Kicks Do Not Claim Growth

Visible kicks are not enough when the drive frequency mismatches.

Visible kicks are not enough when the drive frequency mismatches. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Off-frequency drive closes the growth claim

The natural frequency is 4 hertz, but the drive frequency is 3 hertz.

fnat=4 Hz,fdrive=3 Hzf_\mathrm{nat}=4\ \mathrm{Hz},\quad f_\mathrm{drive}=3\ \mathrm{Hz}
Off-frequency driveThe match flag is no.f0=4 Hzfdrive=3 HzkickTotal=8 Jaccepted=0 Jmatch=nokick1=2 Jkick2=2 Jkick3=2 Jkick4=2 J

Visible kicks do not imply coherent growth

Even with four visible kicks, the accepted growth is exactly 0 joules.

accepted=0 J\mathrm{accepted}=0\ \mathrm{J}
Rejected growth ledgerThe toy ledger rejects off-frequency growth.f0=4 Hzfdrive=3 HzkickTotal=8 Jaccepted=0 Jmatch=nokick1=2 Jkick2=2 Jkick3=2 Jkick4=2 J