Phase Is a Checked State Ledger

Phase Shift Changes Velocity Sign

Quarter-cycle states carry opposite velocity signs. 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 quarter cycle has negative velocity

The checked phase 1/4 has velocity negative 4 metres per second.

ϕ=14⇒v=−4 m/s\phi={1\over 4}\Rightarrow v=-4\ \mathrm{m/s}
Negative velocity phaseThe velocity sign is part of the finite state.A=4 momega=1 1/sphase=1/4x=0 mv=-4 m/sa=0 m/s^2

Three quarters has positive velocity

The checked phase 3/4 has velocity positive 4 metres per second.

ϕ=34⇒v=4 m/s\phi={3\over 4}\Rightarrow v=4\ \mathrm{m/s}
Positive velocity phaseOnly the phase changed, and the sign followed it.A=4 momega=1 1/sphase=3/4x=0 mv=4 m/sa=0 m/s^2