Definition of free vibration: Free vibration is a type of vibration in which a force is applied once and the structure or part is allowed to vibrate at its natural frequency.
Free vibration occurs only in a vacuum because the presence of the air provides some resistance due to which the vibration amplitude does not remain constant and decreases continuously.
Therefore, we define free vibration as the occasional vibration of a constant amplitude body where there is no external force on it.
Hence, a body executes the free vibrations in a vacuum only.