An antenna control system was analyzed in Problem P$4\mathrm{.}5,$ and it was determined that, to reduce the effect of wind disturbances, the gain of the magnetic amplifier,

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should be as large as possible. $($a$)$ Determine the limiting value of gain for maintaining a stable system. $($b$)$ We want to have a system settling time equal to $1\mathrm{.}5$ seconds. Using a shifted axis and$$the Routh$$Hurwitz criterion, determine the value of the$$gain that satisfies this requirement. Assume that the complex roots of the closed$-$loop system dominate the transient response. $($Is this a valid approximation in this case?$)$