In SHM, if the displacement is at its maximum positive value, what can be said about the direction of the acceleration?
**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. Acceleration in SHM is a = -ω² x . At maximum positive displacement ( x = A ), a = -ω² A , which is negative, meaning it acts towards the mean position. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and
Ref: NCERT > Physics Book > Oscillations > Periodic Motion and SHM Basic Concepts