In the previous Sect. 2.1, the single degree-of-freedom (SDOF) system (or oscillator) was examined, after stating the equation of dynamic equilibrium followed by a definition of the characteristics and motion of such a system. In here, we introduce mechanical systems which are defined by more that a single degree-of-freedom (DOF) and as such present a more advanced description of the dynamic response of real structures. These are known as mutiple degree-of-freedom (MDOF) systems whose equations of dynamic equilibrium are derived by the same considerations given to SDOF systems, the difference being that we now have matrix differential equations to contend with instead of a single ordinary differential equation. The most common way to derive the equations of motion is by using Newton’s law of equilibrium of forces in conjunction with the free body (FBD) of the system. As before, the next step is to consider in detail is the solution of such systems for various categories of external forces.