$1.$ An eccentric cam, $100$ mm in diameter, rotates with an eccentricity of $10$ mm as shown in Fig$\mathrm{.}1.$ The roller follower is held against the cam by means of a helical compression spring. The force between the cam and the follower varies from $100$ N at the lowest position to $350$ N at the highest position of the follower. Design the spring from static considerations and determine the factor of safety against fluctuating stresses. Neglect the effect of inertia forces. Use ASTM A$229$ oil tempered steel after set removal as wire material. $($Modulus of rigidity $\backslash (=81370\backslash$mathrm$\{$MPa$\}\backslash ))$