E $7\mathrm{.}7$ The elevator in a modern office building can travel at a speed of $25$ feet per second and is still able to stop within one$-$eighth of an inch of the floor outside. The loop transfer function of the unity feedback elevator position control is

L$($s$)=$G$\_($c$)($s$)$G$($s$)=($K$($s$+8))/($s$($s$+4)($s$+6)($s$+9))$

Plot the root locus for the closed loop system.

Determine the gain K when the complex roots have a equal to $0\mathrm{.}7$