Free-body diagrams

In order to use Newton's second law of motion it is necessary to determine the forces acting on a body so that the resultant force (F) can be found. Thus a system of objects such as springs, dampers and masses should be divided up into its separate components

There are equal and opposite forces (F) at the ends of each the spring and damper.

The free body diagram of the mass m1 is thus,

If we now apply Newton's second law we obtain the equation of motion of the mass m1 as,

and the free body diagram of the mass m2 is,

and the equation of motion of the mass m1 is,