Extended Relativistic Dynamics (ERD) admits only solutions which
have speed bounded by the speed of light c and acceleration bounded
by an assumed universal maximal acceleration a_m. Here we explore
the harmonic oscillator under ERD. The effective potential in this
model becomes linearly confined. For an oscillator with small natural
frequency ω, we recover the classical solutions, while for large ω, the
behavior is quantum-like. The solutions for large ω are a "digitiza-
tion" of the standard signals of the classical harmonic oscillator. The
spectrum of these signals coincide with the energy spectrum of the
quantum harmonic oscillator. While for small ω the thermal radiation
is a wave type, for for large ω it become pulses of radiation. This
provides a possible explanation for the difference in the blackbody ra-
diation for small and large ω and is another indication of the validity
of ERD.