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). Maximum acceleration: aₘₐₓ = ω² A . A = 8 m, ω = 2π s⁻¹ . aₘₐₓ = (2π)² × 8 ≈ 39.48 × 8 ≈ 315.84 m/s² . Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E =