$1.$ Two Helical compression springs are arranged concentrically. The steel springs have a static loading of $3$ kN $.$ If the two springs have the same loaded and unloaded length, a ratio of mean diameters of $3/5$ and a ratio of wire diameters of $5/9.$ Do the following:

a$.$ Calculate the mean diameter of the outer spring if the inner spring has a mean diameter of $30$ mm $.$

b$.$ Calculate the wire diameter of the inner spring if the outer spring has a wire diameter of $9$ mm $.$

c$.$ If presetting was used, and the wire material is ASTM A$229($oil tempered$),$ calculate the allowable shear stress for each of the springs.

d$.$ If the total number of coils for the outer spring is $7$ and for the inner spring is $12$ calculate the spring constant for each spring.

e$.$ Calculate the deflection from the given load for each spring.

f$.$ Calculate the shear stress in each spring for the given load.