Which function represents SHM? (\( \omega \) is a positive constant)
**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. SHM requires a = -ω² x : (a) 5 cos (3ω t + (π/6)) : a = -5 (3ω)² cos (3ω t + (π/6)) = -ω² x , SHM. (b) sin ω t + cos 2ω t : Not SHM (mixed frequencies). e⁻ω t : Not periodic. (d) sin² ω
Ref: NCERT > Physics Book > Oscillations > Periodic Motion and SHM Basic Concepts
