The vibrations of a continuous system under the action of time varying forces are governed by a non-homogeneous partial differential equation. The solution to the governing equation must in addition satisfy certain prescribed conditions on the boundary of the domain. Procedures for the formulation of governing equations and boundary conditions were presented in Chapter 14. Free-vibration response was discussed in Chapter 15. It was indicated there that the equation governing undamped free vibrations reduces to an eigenvalue problem the solution of which provides the eigenvalues or frequencies and eigenfunctions or mode shapes of the system. In this chapter we focus on techniques for the analysis of forced-vibration response. As in previous chapters, we restrict our discussion to systems in one-dimensional space in which the response is a function of one spatial coordinate and the time variable.