The complimentary solution correspomds to the free vibration response and is

dependent on initial conditions.It decays with time as a consequence of damping.Right?

Now, the particular solution is the outcome of the applied force which is influenced by damping and the amplitude of the steady state vibration is more in an undamped system and less in a damped system.Right?

My questions:

1)Consider the particular solution which exists as a result of the applied force.Suppose if we continue to apply the force for a very lng time "t", will damping continue causing the lowering the amplitude of the response upto this time "t" at the same rate?Why?

2) Also, it has been observed that lighter the damping , more is the number of cycles required to achieve a steadt state response, i.e. the amplitude of the deformation being constant.What does this signify???