Phase is not the same as path distance
- 01
The tempting model
Confusing where an oscillator is in its cycle with how far it has traveled.
- 02
Why it feels right
Both phase and distance mark progress through motion.
- 03
Where it breaks · how to catch it
You use arc length or total path traveled to decide whether two oscillators are in phase.
- 04
The correct model
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.
- 05
Repair · see it, then test it
worked example A mass returns to its starting point after one period. What is its phase difference?
Tempting move
Nonzero because it traveled 4A.
Correct move
Zero modulo 2π; it is in the same state again.
Test the repair SHM-05 · transferMake a fresh prediction before referring to the worked example.