← all cardsTopic 8 · Oscillations · State of motion & graphs
Quarter-period gaps
Max speed (at centre) and the next max acceleration (at an extreme) are separated by T/4 — adjacent special points are always a quarter period apart: centre → extreme → centre → other extreme, each step T/4.
What this actually means
The special points of the motion alternate every quarter period: centre (max speed), extreme (max acceleration), centre again, other extreme. Each hop is T/4.
So maximum speed and the next maximum acceleration are T/4 apart, and consecutive passes through the centre are T/2 apart. Timing questions are usually just counting these hops.
Prove it — watch it be true
- STEP π/4 twice: exactly a quarter period has passed
- The shadow has moved centre to extreme: max speed point to max acceleration point
- Two more steps: back to the centre — every hop is T/4