  The harmonic oscillator plays a central role in physics describing the
dynamics of a wide range of systems close to stable equilibrium points. The
nonrelativistic one-dimensional spring-mass system is considered a prototype
representative of it. It is usually assumed and galvanized in textbooks that
the equation of motion of a relativistic harmonic oscillator is given by the
same equation as the nonrelativistic one with the mass $M$ at the tip
multiplied by the relativistic factor $1/(1 - v^2/c^2)^{1/2}$. Although the
solution of such an equation may depict some physical systems, it does not
describe, in general, one-dimensional relativistic spring-mass oscillators
under the influence of elastic forces. In recognition to the importance of such
a system to physics, we fill a gap in the literature and offer a full
relativistic treatment for a system composed of a spring attached to an
inertial wall, holding a mass $M$ at the end.
