A single$-$cylinder engine with a mass of $300$ kg is mounted on $4$ shock absorbers$.$ When each shock absorber was left to damped vibration after assembly, $45$ full oscillations were completed in $7$ seconds. The stroke of the engine is $72$mm$.$ Calculate the spring constant of all shock absorbers$.$

B$)$ Calculate $($c$)(\backslash$xi $)$ the damping degree and damping constant of the shock absorbers$.$

C$)$ When the engine was started at $5200$ rpm$,$ the vibration amplitude was measured as $4$ mm$.$ What is the amount of mass moving back and forth in this situation?

E$)$ At what speed should it be operated to reduce the force transmitted to the ground by half?