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). Acceleration: a = -ω² x . ω = 4 s⁻¹, x = 3 sin (4 × 0.25 + (π/3)) = 3 sin (1 + (π/3)) ≈ 3 sin 1.571 ≈ 3 m . a = -4² × 3 = -16 × 3 = -48 m/s² . Applying x