The control rod $AC$ is guided by two pins that slide freely in parallel curved slots of radius $202$ mm $.$ The rod has a mass of $9\mathrm{.}8$ kg $,$ and its mass center is located at point $G.$ Knowing that for the position shown the vertical component of the velocity of point $C$ is $1\mathrm{.}22\frac{m}{s}$ upward and the vertical component of the acceleration of point $C$ is $5\mathrm{.}08\frac{m}{s^2}$ upward, determine the magnitude of the force $P.$ Note that the acceleration of point $C$ comprises both tangential and normal components.