Practice question

**Periodic motion** repeats after fixed period T, x(t+T)=x(t), while oscillatory motion involves to-and-fro about equilibrium. SHM is special periodic motion where restoring force proportional to displacement, F = -k x, acceleration a = -ω² x, leading to sinusoidal displacement x = A cos(ωt + φ). For SHM, a = -ω² x . Given a = -25 x , ω² = 25 ⇒ ω = 5 rad/s . Frequency: v = (ω/2π) = (5/2 × 3.14) ≈ 0.796 Hz . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.796 Hz follows,