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. Velocity: v = -ω A sin (ω t) . ω = 6 s⁻¹, vₘₐₓ = ω A = 15 ⇒ A = (15/6) = 2.5 m . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result 2.5 m follows, reflecting SHM dependence on amplitude A, ω and system parameters.