Problem 4 A cassette tape storage device has been designed for mass- storage. It is necessary to control the velocity of the tape accurately. The speed control of the tape drive is represented by the system shown in Figure 3. (a) Determine the range of gain K for a stable system. (b) Determine a suitable gain so that the overshoot to a step command is approximately 5%. R(s) Power amplifier K Motor and drive mechanism 10 Y(s) s+ 100 (s +20)² Speed Figure 3