Nowadays scientists are working on removing the destructive effect of vibration phenomenon that has unfavorable effect on industrial devices which can be harmful or can destroy them. This can be done by changing the physical parameters or using more accurate methods of solution. To improve the useful life time of machines, vibration should be controled or removed. In vibration study, linear model of the system can be incorrect or misleading. Nonlinear characteristics in a mechanical system may cause vibration behaviors that cannot be seen or predicted when the system modeled linearly. Also fighter aircraft have reached the stage where the time spent at high angles of attack is a substantial fraction of the total flying hours. Depending on the angle of attack and freestream velocity, vertical flow impinges on the tail and creates large dynamic responses, which result in large dynamic loads and stresses throughout the tail structure. Thus, emphasis on the twin-tail buffeting has increased. Buffeting is defined to be the response of an aircaft or airframe component to the random aerodynamic load. These severe random pressure environments can cause shortened structural fatigue lives and premature structural failure as in the case of the F-15 and F-18 aircraft. Thus, it is important to reduce the unwanted vibrations caused by buffet loads and thus extend the fatigue life of the vertical tails. A common and very effective way to reduce buffeting is to increase the amount of damping in the system, thereby achieving greater energy dissipation. Passive or active techniques can be used to achieve such a goal. Passive techniques can be implemented by modifying the structureproperties of the vertical tail: structural dampings, damping links, tuned mass dampers, interface damping and solidspace damping. In this work the twin-tail of a military plane is modeled as a two degrees of freedom system with quadratic and cubic nonlinear terms under harmonic excitation. This system has linear and quadratic damping terms. Vibration equations of the system that are nonlinear differential equations, are solved using perturbation method such as the method of multiple time scales. Different cases of primary and secondary resonances are investigated and effects of system parameters on the behavior of the system are studied. The system is actively controlled by negative (linear, cubic) velocity feedback. Also the results of feeding back the velocity and its cube compared. Because of the interaction between the two tails, it is important to employ a separate controller for each tail to suppress the vibrations of both tails. Finally, the instantaneous power requirements of both techniques compared. Keywords: Nonlinear vibration, External excitation, Primary and secondary resonant, Multiple time scales method