A fragile item A, with weight W, is to be shipped within a box B using the vertical spring...

A fragile item A, with weight W, is to be shipped within a box B using the vertical spring suspension shown. Springs 1 and 2 have stiffnesses k1 and k2, respectively, and unstretched lengths L1 and L2, respectively. The springs are installed by stretching them to the same length h and then attaching them to A. The vertical deflection δ is measured such that δ = 0 is the position where A is in the middle of box B.

(a) Show that W and δ are related by

(b) Explain why δ ≠  0 when W = 0.

(c) Suggest some mathematical tests you can perform to verify the accuracy of the expression in Part (a). For example, if δ = 0 and k2 = 0, show that W has the expected value.