  We reformulate Classical Mechanics as a timeless relativistic theory. Readers
are introduced to a new class of reference systems, the binate frames, where
physical events are identified with four position-coordinates -- no clocks are
used. The binate frames are inertial and adaptable to relative motions.
Analyses that use binate frames are valid at all energy levels. When desirable
to do so, the results are easily expressed as in special relativity, in terms
of space and time coordinates of inertial observers. Given the importance of
mass-and-spring systems to theoretical physics, we analyzed such a system.
Published special relativistic solutions predict anharmonic oscillations, but
in the inertial frame where the mass-and-spring system (as a whole) is at rest,
our solution is harmonic with energy-dependent angular frequency.
