For a compression spring with 1 inch OD was made by 0.1inch diameter hard-drawn wire. The spring with 6inch free length has squared end and is peened. The spring was compressed to 5 inch (a kind of pre-load condition) (hint: Fmin is not zero) during machine installation. Then, the spring is used in a machine by compressing it from 5inch (pre-compressed) into a solid length of 4 inch. Determine:
a. Spring rate
b. the fatigue factor of safety when repeatedly cycled from 5-inch length (pre-load condition) to solid length.

In a unit cell of fcc structure, indicate the position of one of the tetrahedral interstitial sites by plotting the corresponding tetrahedron. do the same for one of the octahedral interstitial sites (in a separate fcc unit cell). mark the positions of all the tetrahedral and octahedral interstitial sites in the unit cells. how many equivalent tetrahedral sites and how many equivalent octahedral sites are contained in a fcc unit cell, respectively. what is the coordination number for a tetrahedral site and what is the coordination number for an octahedral site?