Velocity vs Time

Velocity in SHM: v(t) = dx/dt = −Aω·sin(ωt + φ).

Maximum velocity v_max = Aω, occurs at equilibrium (x = 0).

Minimum velocity (= 0) at extremes (x = ±A).

Energy view: KE = ½mv² maximum at center, zero at extremes.

v vs x relation: v² = ω²(A² − x²) ⇒ v = ω·√(A² − x²).

v leads x by π/2 in phase (v = Aω cos shifted by 90° from x = A sin).

On v-x phase plot: ellipse with semi-axes A (x) and Aω (v).

Used in calculating KE distribution and timing of SHM events.