In the preceding chapter, the free undamped and damped vibration of single degree of freedom systems was discussed, and it was shown that the motion of such systems is governed by homogeneous second-order ordinary differential equations. The roots of the characteristic equations, as well as the solutions of the differential equations, strongly depend on the magnitude of the damping, and oscillatory motions are observed only in underdamped systems. In this chapter, we study the undamped and damped motion of single degree of freedom systems subjected to forcing functions which are time-dependent. Our discussion in this chapter will be limited only to the case of harmonic forcing functions. The response of the single degree of freedom system to periodic forcing functions, as well as to general forcing functions, will be discussed in the following chapter.