Is there a physical conceivable situation where a radioactive atom vibrates, and still have enough time to increase his vibration frequency before dacaying?
Vibration of the electron of an atom or of the mode shape(s) of a molecule, or mean free path of an atom or molecule, are baseline concepts of temperature or thermal Kinetic Energy (KE). Atomic vibration or temperature modeled at this level is typically independent of radioactive decay processes, which take place or are dominated by processes in the nucleus of the atom, i.e. nuclear processes. The exception would be for a high enough bulk decay rate in the material that the emitted particles deliver heat as they are absorbed in that bulk material, resulting in temperature change (i.e. nuclear power generation reactor or nuclear bomb).
Atomic or molecular vibratory modes would have time to evolve if the half life of the isotope is long enough, typically the case for all stable or even semi-stable isotopes.
Thermal vibration at molecular level is modeled by science called Molecular Dynamics or "MD", so you should take a look at some MD papers to see how these things may or may not relate to your interest.
Also, there are transient oscillations in the molecular dynamic environment, such as after passage of a shock wave, where there are discontinuous conditions placed upon the molecule and a non-steady state response results, i.e. a transient oscillation. The time scales of these transients are typically short for shock experiments in the lab, but may become extended in larger scale situations such as planetary impact, where the overall bulk material is bathed in high KE delivered by the shock, where associated transient behavior and damping of the transient portion of oscillation becomes delayed. This transient-rich oscillation state is known as "shock disorientation", during which time temperature is undefined to some degree, an interesting concept all by itself. MD is good brain food.
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