EL on L = mv²/2 − kx²/2: equation k·x + m·ẍ = 0, residual ≡ 0 on A·cos(ωt+φ)

Exact symbolic application of the Euler-Lagrange equation to the harmonic-oscillator Lagrangian L = m·ẋ²/2 − k·x²/2. Computation: ∂L/∂ẋ = m·ẋ; d/dt(m·ẋ) = m·ẍ; ∂L/∂x = -k·x. The Euler-Lagrange equation d/dt(∂L/∂ẋ) − ∂L/∂x = m·ẍ + k·x = 0…