The Q-factor tells you something about the frequency response of a drive**n** system to a constant amplitude drive**r** when a steady state (constant amplitude of drive**n** system) has been reached.  
The drive**r** supplies energy to the drive**n** system which at steady state results in the energy stored in the drive**n** system staying constant (constant amplitude) and there is also a constant rate of energy (power) dissipation from the drive**n** system..
 
With a non-driven system there is no input of energy into the system and so the energy (amplitude) of the oscillating system just decreases with time.