VeMMA — Velocity and Acceleration in SHM

Velocity is Max at Mean; Acceleration is max at Amplitude. At x = 0: v = Aω (max), a = 0. At x = ±A: v = 0, a = Aω^{2} (max). Always opposite.

"Closed pipes are Odd" (CPAO)

Closed Pipe = Odd harmonics Only. 1, 3, 5, 7… Never even. Open pipes play All.

Doppler "TTop BBottom"

Toward observer (numerator = Top): add $v_O$ → f' rises. Toward source (denominator = Bottom): subtract $v_S$ → f' rises. Away = opposite sign in each.

"SHM Square Root Two" for Energy Equality

KE = PE at x = A/√2 — the "√2" in the denominator. Not "half", but "half squared".

Spring Series vs Parallel — "Series Softens, Parallel Powers"

• Series → Softer spring (lower $k_{eff}$) → Slower oscillation (longer T)
• Parallel → Powerful spring (higher $k_{eff}$) → Punchier oscillation (shorter T)

Speed Order — "GSL" (Gas, Solid, Liquid reversed)

$v_{solid}$ > $v_{liquid}$ > $v_{gas}$. Remember: the REVERSE alphabetical of G-S-L.

Nodes distance — "Half a Lambda"

Consecutive nodes (or antinodes) are always λ/2 apart. Half wavelength = node spacing.