The degrees of freedom (D of F) of a system are the minimal set of variables needed to define the configuration of the system at a given instant in time. Note that because we wish to describe only a given instant in time, quantities which involve changes in time, such as velocities, need not be specified.
In the example of the SHO (Figure 1), we only need
one variable, the position of the mass x to define the configuration
of the system at any given time t. There is thus only one degree of
freedom in our present system, x(t)
.