Holding period fixed makes phase a scan of lag divided by period. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Three seconds of twelve is one quarter cycle
Period 12 seconds and lag 3 seconds give phase 1/4 cycle.
123=41 cycle
Six seconds of twelve is one half cycle
Keeping the period at 12 seconds, lag 6 seconds gives phase 1/2 cycle.
126=21 cycle
Nine seconds of twelve is three quarters cycle
Lag 9 seconds over period 12 seconds gives phase 3/4 cycle.