| Cue / Question | Notes |
|---|---|
| What is SHM? | Periodic motion where restoring force ∝ displacement toward mean: a = -ω^{2}x |
| SHM displacement formula? | x = A sin(ωt + φ) — Amplitude A (m), ω = angular frequency (rad/s), φ = phase |
| Velocity in SHM? | v = ω√( - ); v_max = Aω at x = 0; v = 0 at x = ±A |
| Acceleration in SHM? | a = -ω^{2}x; a_max = Aω^{2} at x = ±A; a = 0 at x = 0 |
| KE = PE condition? | At x = A/√2 (NOT A/2); KE = PE = E/2 = ¼mω^{2} |
| Total energy in SHM? | E = ½mω^{2} = constant throughout motion |
| Spring-mass period? | T = 2π√(m/k); independent of amplitude and gravity |
| Pendulum in free fall? | g_eff = 0 → T = ∞ → no oscillation |
| Wave speed formula? | v = fλ = ω/k; string: v = √(T/μ); air: v ∝ √T_kelvin |
| Standing wave nodes? | Nodes at x = nλ/2; antinodes at x = (2n+1)λ/4 |
| Closed pipe harmonics? | ODD ONLY: n = 1, 3, 5…; f_{1} = v/(4L); first overtone = 3rd harmonic |
| Open pipe harmonics? | ALL: n = 1, 2, 3…; f_{1} = v/(2L); same as vibrating string |
| Doppler formula? | f' = f(v ± v_O)/(v ∓ v_S); toward → higher f; away → lower f |
| Beat frequency? | f_beat = |
Summary: SHM is governed by a = -ω^{2}x, with energy conserved as ½mω^{2}. Key NEET traps: KE = PE at x = A/√2 (not A/2), closed pipes produce only odd harmonics (f_{1} half that of open pipe of same length), and Doppler sign convention (+ numerator toward, − denominator toward). Wave speed in string v = √(T/μ); in air v ∝ √T_K. Standing waves: nodes at nλ/2, antinodes at (2n+1)λ/4.