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 = 3 s⁻¹, x(0) = 6 sin (-(π/4)) = -6 sin (π/4) = -6 × (√(2)/2) ≈ -4.24 m . a = -3² × (-4.24) = 9 × 4.24 ≈ 38.16 m/s² . Applying x = A cos(ωt + φ), v