This paper presents the results of a general study that has been made of a linear system having 2 deg of freedom. This is representative for many mechanical vibration problems as well as for problems of other physical systems. The system is described specifically in terms of the mechanical parameters of translational motion and consists of one mass, spring, dashpot system mounted on another. Three types of generalized solutions are given for the maximum motion of the first system relative to the second, or the maximum stress developed in the spring of the first system. One of these is for known sinusoidal forces applied to the second system, one is for the whole system striking a fixed base at a known velocity without rebound, and one is for such an impact and one rebound. The solutions were obtained on the mechanical transients analyzer which employs the principle of electric-circuit analogy. The solutions are given in dimensionless curve form for a wide range of all parameters.