Particle state checklist (SHM on a wave)
● VERBATIM — examined word-for-wordEvery point performs SHM: speed max at equilibrium crossings, zero at crest/trough; acceleration a = −ω²y — max at extremes, towards equilibrium, zero at equilibrium; energy all-kinetic at centre, all-potential at extremes. All points share the same amplitude and energy (1-D, no losses). Chains straight back to Topic 8.
What this actually means
Every particle on a wave is a Topic 8 oscillator, so the whole SHM state table transfers: speed max at zero displacement and zero at the extremes; acceleration max at the extremes and always aimed at equilibrium.
Energy trades between kinetic (through the centre line) and potential (at the extremes), with a constant total per particle.
In an ideal 1-D wave with no losses, every particle carries the same amplitude and hence the same energy. Amplitude only decays through spreading (2-D or 3-D geometry) or damping.
Prove it — watch it be true
- Pick a particle at a crest: velocity arrow zero, about to accelerate downwards
- Pick one crossing equilibrium: velocity arrow at its longest
- STEP T/8 and watch each particle run the full SHM cycle