Here's the situation: both springs are compressed by an amount x0. The rod of length L is xed to both the top plate and the bottom plate. The two springs, each with spring constant k, are wrapped around the rod on both sides of the middle plate but are free to move, because they are not attached to the rod or the plates. The middle plate has negligible mass, and is constrained in its motion by the compression forces of the top and bottom springs. The medical implementation of this device is to screw the top plate to one vertebrae and the middle plate to the vertebrae directly below. The bottom plate is suspended in space. Instead of fusing broken vertebrates together, this implant allows movement somewhat analogous to the natural movement of mctioning vertebrae. Below you will do the exact calculations that an engineer did to get this device patented and available for use at hospitals. a. Find the force, F, on the middle plate for the region of its movement Ax 5 x0 . Give your answer in terms of the constants given. (Hint: In this region both springs are providing opposite compression forces.) b. Find the force, F, on the middle plate for the region of its movement Ax 2 x9. Give your answer in terms of the constants given. (Hint: In this region, only one spring is in contact with the middle plate.) c. Graph F vs. x. Label the values for force for the transition region in terms of the constants given