E. (26%) Disk-storage devices are used with computers. The data head is moved to different positions on the spinning disk and rapid, accurate response is required. A simplified block diagram of a data-head positioning system is shown below. a (13%) Find the closed loop system transfer function H(s). b. (13%) Determine the range of the value a in the controller for which the system is stable. Desired position f(t) + Controller 5(s+a) (s+1) Head dynamics (s+4) Data head position y(t) 2. Virtual Memory is commonly used memory management technique that uses hardware and software to allow a computer to compensate for physical memory shortages by temporarily transferring data from the main memory to the secondary memory. Paging and Translation Lookaside Buffer are always used in virtual memory. Meanwhile, the virtual memory mechanism must interact with the cache system. Illustrate the detailed work flow of one data fetch operation with all possibilities. (10 points) (Mechanisms you need to include: Reference, Page, Page table, TLB, main memory, disk, cache)