Repeat Problem 14 of Problem Set 5.3, using Lagrange's equations.

Data From Problem 14 From Problem set 5.3:

Repeat Problem 13 for the system shown in Figure 5.72, in which each pendulum is a uniform slender rod of mass m and length L. The inputs are the torques τ1 and τ2 applied to the pivots O1 and O2, respectively. When θ1 = 0, θ2 = 0, τ1 = 0, and τ2 = 0, the spring is at its free length.

FIGURE 5.72 Problem 14. L/3 01