A solid cylinder of mass \(M\) and radius \(R\) has a rotational inertia \(I = \dfrac{1}{2}MR^2\). The cylinder is mounted on a fixed, frictionless horizontal axle that passes through its center. A nonlinear torsion spring, coiled around the axle, connects the cylinder to a fixed support. When the cylinder is rotated by an angle \(\theta\) from its equilibrium position at \(\theta = 0\), the spring exerts a restoring torque \(\tau\) on the cylinder given by the function \(\tau(\theta) = -C \theta^3\), where \(C\) is a positive constant. The cylinder is rotated to a positive initial angle \(\theta_0\) and held at rest.