  Using the Liouville space framework developed in nonlinear optics we
calculate the linear response functions and susceptibilities of Bose-Einstein
condensates (BEC) subject to an arbitrary mechanical force. Distinct signatures
of the dynamics of finite temperature BEC are obtained by solving the
Hartree-Fock-Bogoliubov theory. Numerical simulations of the position dependent
linear response functions of one dimensional trapped BEC in the time and the
frequency domains are presented.
