Acceleration vs Time

Acceleration in SHM: a(t) = dv/dt = −Aω²·cos(ωt + φ) = −ω²·x.

Maximum |a| = Aω², at the extremes (x = ±A).

ZERO at equilibrium (x = 0).

Always points TOWARD the equilibrium position (restoring nature).

a vs x: linear with negative slope (a = −ω²x). On an a-x graph: straight line through origin with slope −ω².

a is in PHASE with −x: when x is at +A, a is at maximum negative value.

Important relation: a + ω²x = 0 — the defining DE of SHM.

Used in finding force, identifying SHM from given motion equations.