Practice question

**Real oscillators** experience damping, amplitude decreasing with time. Critical damping returns to equilibrium fastest without oscillation, overdamping slows return, underdamping shows decaying oscillations, classification based on b relative to 2mω₀, important for practical systems. T = 2π √((m/k)) . 0.4 = 2π √((m/100)) ⇒ (0.4/2π) = √((m/100)) . ((0.4/6.28))² = (m/100) ⇒ m = 100 × (0.0637)² ≈ 0.405 kg . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.405 kg follows, reflecting SHM dependence on amplitude A, ω and system parameters.