On the Worst-Case Disturbance of an Oscillator with Quadratic Damping by an External Force with a Given Integral

The problem of constructing the worst-case disturbance for an oscillator with quadratic damping is considered. The disturbance is carried out by an external force, which is applied to the oscillator body, does not change the direction of its action and has a given impulse (time integral). It is assumed that before the onset of the disturbance the oscillator is in a state of equilibrium. The worst disturbance is considered to be one in which the absolute value of the displacement of the oscillator body from the equilibrium position reaches its maximum value. In the class of disturbances of a rectangular profile with a given impulse, the worst disturbance and the corresponding largest displacement and the time to reach it were found, depending on the parameters of the oscillator.