Note that frequency response is defined as the response of the system when the input is a sinusoid, i.e., when u(t)=A sin Wt. So when we talk about the frequency response of a system like, say, x''-2zwx'-w2=u(t), we mean that we are interested in determining x(t) when u(t)=A sin Wt. Therefore, saying "frequency response of the system x''-2zwx'-w2=u(t), when u(t)=0" does not make sense. This is just like the definition of "step response" or "impulse response". In these cases, u(t) is chosen to be a step or an impulse, respectively.