In Chapter 1, the response of a single degree of freedom (SDOF) system to free and forced vibration under a harmonic force was investigated. It was shown that for lightly damped systems, the frequency is dependent mainly on the mass and stiffness of the system. It was also shown that i f the frequency of the applied force is nearly equal to the natural frequency of the system then the system resonates resulting in very large displacements. In this chapter the response of the SDOF system to general loads will be investigated and methods both analytical and numerical will be described for solving the differential equation viz.