Vibration systems consisting only of inert or only elastic elements and the appearance of free harmonic vibrations in them

We consider mechanical vibration systems consisting only of inert ($mm$-, $mmm$-, $m^n$-systems) or only elastic ($kk$-, $kkk$-, $k^n$-systems) components. The possibility of the of free harmonic vibrations appearance in such systems is shown. In the $mm$-, $mmm$-, $m^n$-systems, the mutual exchange of kinetic energy between the inert elements occurs; in $kk$-, $kkk$-, $k^n$-systems, the mutual exchange of the potential energy between elastic elements.