Repeat Problem 13 of Problem Set 5.3, using Lagrange's equations.

Data From Problem 13 From Problem set 5.3:

Consider the two-degree-of-freedom system shown in Figure 5.71, in which two simple inverted pendulums are connected by a translational spring of stiffness k. Each pendulum consists of a point mass m concentrated at the tip of a massless rope of length L. θ1 and θ2 are the angular displacements of the pendulums. When θ1 = 0 and θ2 = 0, the spring is at its free length.

FIGURE 5.71 Problem 13. m m