The jet engine (mass m = 400kg) of a passenger airplane is attached to the plane's wing by a connector that has an effective stiffness of k = 640 x 10^9 N/m and an effective damping coeffcient of c = 3.0 x 10^6 N ·sec/m. In order to save weight the connector is designed with a natural frequency that is smaller than the jet engine's nominal operating frequency, which is w = 8 x10^4 rad/sec. This means that when the engine is powered up it will produce a forcing function that acts on the connector and resonance will occur when the engine reaches the connector's natural frequency. This would cause the connector to experience large deformations and possibly fail.
To avoid such a failure, the connector design calls for a hydraulic stiffener that will temporally increase the connector's stiffness and therefore its natural frequency. The stiffener acts in parallel with the connector and is activated when the engine frequency reaches 70% of the connector's natural frequency (without the stiffener). Once the engine reaches a frequency of 120% of the connector's natural frequency the stiffener is turned off.
Determine the required stiffness k of the hydraulic stiffener such that the response amplitude C/fo of the connector does not exceed 2 during the jet engine power up.