Practice question

**Resonance phenomenon** amplifies response when driving frequency matches natural frequency ω_d ≈ ω₀, large amplitude even with small F₀, as damping limits growth. Natural frequency determined by system parameters, resonance condition crucial for understanding vibrations and energy absorption, e.g., bridge collapse, tuning. For SHM, a = -ω² x . Given a = -36 x , ω² = 36 ⇒ ω = 6 rad/s . Frequency: v = (ω/2π) = (6/2 × 3.14) ≈ 0.955 Hz . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 0.955 Hz follows, reflecting SHM dependence