A general solution of the equations of forced motion of a harmonic crystal or other vibrating system with arbitrary time-dependent forces acting on the atoms is given. The solution is given in terms of dynamical "response functions", for which expressions in terms of the normal mode frequencies and eigenvectors (polarization vectors) are given. Numerical calculations of the response functions are described for (111) and (100) surfaces of face-centered cubic crystals interacting with Lennard-Jones 6-12 potentials, and the qualitative features of the surface and bulk response functions are discussed. The use of these functions in problems of atomic scattering from surfaces is outline, and conveneint parameterized forms for this application are given. © 1978.