Simple Harmonic Motion is defined by the equation a = −ω^{2}x, where the restoring force is proportional to and directed against the displacement from equilibrium. The sinusoidal displacement x = A sin(ωt + φ) yields a velocity v = ω√($A^{2}$ − $x^{2}$) that is maximum at the mean position and zero at the extremes. Total mechanical energy in SHM, E = ½mω^{2}$A^{2}$, is constant, with KE equalling PE at x = A/√2 — not x = A/2, which is a frequent NEET trap. The spring-mass system has period T = 2π√(m/k), independent of amplitude and gravity, while the simple pendulum T = 2π√(L/g) depends on gravity and fails in free fall. Wave motion transfers energy without net matter transport, described by y = A sin(kx − ωt) for a progressive wave. Wave speed in a string is v = √(T/μ); in air, v = √(γRT/M) ∝ √T_K, with the order v_solid > v_liquid > v_gas. Superposition of two identical counter-propagating waves produces standing waves with nodes at x = nλ/2 and antinodes at x = (2n+1)λ/4. Open organ pipes and strings support all harmonics f_n = nv/(2L), while closed organ pipes support only odd harmonics f_n = nv/(4L) with fundamental half that of the open pipe. When two waves of slightly different frequencies interfere, beats are produced at f_beat = |f_{1} − f_{2}|. The Doppler effect gives apparent frequency f' = f(v ± v_O)/(v ∓ v_S), with toward-motion increasing and away-motion decreasing the perceived frequency.