  In this work we consider a dynamic system consisting of a damped harmonic
oscillator and we formalize a Turing Machine whose definition in terms of
states, alphabet and transition rules, can be considered equivalent to that of
the oscillator. We prove that the Turing Machine of a FOR loop corresponds to
that of the oscillator and we ask ourselves if it is possible to obtain the
dynamic system of the harmonic oscillator as a physical realization of the FOR
loop. We discuss the relationship between the results found and the science of
Can and Can't. We discuss the possibility of an evolution of computer science
also towards non-computerized specialized machines whose operating principle is
designed as an automatic process starting from a source code instead of as a
work of human ingenuity. The approach to the implementation of algorithms in
dynamic systems instead of universal computers can be particularly interesting
for the field of both diagnostic and implantable medical devices.
