For a system with the following Lagrangian function: E M L = 2 2.2 k x2 + 2 2 (1) calculate the frequency of free oscillations as a function of their amplitude a. Use the van der Pol method of perturbative expansion x(t) = x1(t)+x2(t)... and w = wo+w₁+w2... to single out the resonant term of frequency w and obtain the harmonic-balance equation by requiring the net amplitude of that frequency component to vanish. You may assume a small parameter ea²/m <<< 1.