Determine the momentum of a simple harmonic oscillator


 * 1) Find the Lagrangian that describes a simple harmonic oscillator: \(\mathcal{L}(x(t), \dot{x}(t))=\frac{1}{2}m\dot{x}^2 - \frac{1}{2}m\omega^2 x^2\)
 * 2) Differentiate this with respect to \(\dot{x}\): \(\frac{\partial\mathcal{L}}{\partial\dot{x}}(x(t), \dot{x}(t))=m\dot{x}\)