$(10$ pts$)$ A $4\mathrm{.}0$ lb electronics system can maximumly withstand a $3$g sinusoidal vibration. The system must pass a vibration test in which the base will be loaded to $12$g and a frequency of$80$ Hz$.$ Assuming a single mechanical spring is used as the vibration isolator which has the damping factor of $10\%,$ what is the maximum desired spring stiffness?$(10$ pts$)$ A $4\mathrm{.}0$ lb electronics system can maximumly withstand a $3$ g sinusoidal vibration. The system must pass a vibration test in which the base will be loaded to $12$ g and a frequency of $80$ Hz $.$ Assuming a single mechanical spring is used as the vibration isolator which has the damping factor of $10\%,$ what is the maximum desired spring stiffness?