Practice question

**Distinction between periodic and oscillatory** clarifies all SHM is periodic but not all periodic is SHM. SHM requires linear restoring force and inertia, a ∝ -x, with ω = √(k/m). Functions like sin²ωt have period π/ω but lack a = -ω² x, thus periodic not SHM, while uniform circular motion is periodic without linear oscillation. For SHM, a = -ω² x . Given a = -81 x , ω² = 81 ⇒ ω = 9 rad/s . Frequency: v = (ω/2π) = (9/2 × 3.14) ≈ 1.43 Hz . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x