Homework H$\mathrm{.}4.$I

Given: Particle P $($of mass $m)$ is constrained to move along a smooth circular guide $($of radius $R).$ A spring of stiffness $k$ is attached between P and the fixed point O $,$ where O is on the same horizontal line as the bottom of the circular guide, as shown in the figure. At position $1,$ P is at rest and is on the same horizontal line as the center of the guide C $.$ At position $2,$ P is on the same horizontal line as O and the spring is unstretched.

Find: Determine the speed of particle $P$ at position $2.$

Use the following parameters in your analysis: $m=50kg,R=0\mathrm{.}6m,d=0\mathrm{.}8m$ and $k=500\frac{N}{m}.$