Solve Problem 39 for the initial conditions \(\theta(0)=0\) and \(\dot{\theta}(0)=\dot{\theta}_{0}\) for two cases of the stiffness:

\[ K>\frac{m g l}{2} \quad \text { and } \quad K<\frac{m g l}{2} \]

What is the solution for \(K=m g l / 2\) ?