Seismic wave control is very important both in civil and mechanical engineering. Common passive methods for isolating a building or a device include Base Isolators (BI) and Tuned Mass Dampers (TMD). In the present paper, a time varying controllable spring is considered as a vibration isolator for a linear mechanical system. The controller works as follows: when the seismic movement is active, the velocity of the moving mass is monitored as the reference velocity. When such reference velocity is positive, the stiffness is reduced; when it is negative, the stiffness is increased. Numerical investigations show that the controller is capable to filter seismic excitation close to the natural frequency of the controlled system, and to reduce the total seismic energy transfer up to 5 times. The role played by the gravity in the active vibration filtering is pointed out by showing that no filtering action can be observed in gravity-free simulations. Even though the controlled system is linear, the controller presents a non-smooth fluctuation of the stiffness, so that a limit cycle occur within the system.