Practice question

**Sinusoidal description** links amplitude A and angular frequency ω to instantaneous values. Given x(t) = A cos(ωt), max acceleration ω²A quantifies force requirement F_max = m ω²A, and velocity at arbitrary x is v = ±ω√(A² - x²) from energy conservation. Maximum speed: vₘₐₓ = ω A . A = 7 m, ω = π s⁻¹ . vₘₐₓ = π × 7 ≈ 3.14 × 7 ≈ 21.98 m/s . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 20.0 m/s follows, reflecting SHM dependence on amplitude A, ω and system parameters.