Phase is not the same as path distance
The mistake
Confusing where an oscillator is in its cycle with how far it has traveled.
Why it feels right
Both phase and distance mark progress through motion.
How to catch it
You use arc length or total path traveled to decide whether two oscillators are in phase.
The first principle
Phase is the angle-like state in the oscillation cycle. Two oscillators separated by one full period in time are in phase even if each traveled a long path.
worked mini-example
A mass returns to its starting point after one period. What is its phase difference?
Common wrong move
Nonzero because it traveled 4A.
Correct
Zero modulo 2π; it is in the same state again.
Test the repair SHM-05 · transfer
Make a fresh prediction before referring to the worked example.