## ABSTRACT

Second-order differential equations arise in many applications. In fact, since acceleration is given by a second derivative, any application requiring Newton’s equation F = ma has the potential to be modeled by a second-order differential equation.

In this chapter, a class of applications involving masses bouncing at the ends of springs is analyzed. This is a particularly good class of examples to be examined at this point. For one thing, the basic model is relatively easy to derive and is given by a second-order linear differential equation with constant coefficients. Hence, the material from the last chapter can be used to derive reasonably accurate descriptions of the motion under a variety of situations. Moreover, most readers already have an intuitive idea of how these “mass/spring systems” behave, and will be able to compare the results derived here with their intuitive notions.

It should also be noted thatmuch of the analysis developed in this chapter for mass-spring systems carries over to the analysis of other applications involving things that vibrate or oscillate in some manner. For example, the analysis of current in basic electric circuits is completely analogous to the analysis carried out here.