A thin circular rod is supported in a vertical plane by a bracket at A. Attached to the bracket and loosely wound around the rod is a spring of constant$\text{k}=40\text{N/m}$ and under formed length equal to arc of the circle AB. A 0.2kg collar ‘C’, not attached to the spring can slide without friction along the rod. The collar is released from rest at an angle$\theta$ with the vertical. Make the equation for minimum value of $\theta$  for which the collar will pass through D and reach point A is $\beta {\theta }^2=1+\cos \theta$ where $\beta =$