Practice question

**SHM kinematics** given by x = A cos(ωt + φ), velocity v = dx/dt = -ω A sin(ωt + φ), acceleration a = dv/dt = -ω² A cos(ωt + φ) = -ω² x, maxima v_max = ωA at mean position x=0, a_max = ω²A at extremes x=±A. Phase φ determines initial position, ω = 2π/T = √(k/m). Velocity: v = ± ω √(A² - x²) . A = 5 m, ω = 2 s⁻¹, x = 2.5 m . v = 2 √(5² - 2.5²) = 2 √(25 - 6.25) = 2 √(18.75) ≈ 8.66 m/s . Applying x = A cos(ωt + φ), v