  The thermodynamic uncertainty relation (TUR) for underdamped dynamics has
intriguing problems while its counterpart for overdamped dynamics has recently
been derived. Even for the case of steady states, a proper way to match
underdamped and overdamped TURs has not been found. We derive the TUR for
underdamped systems subject to general time-dependent protocols, that covers
steady states, by using the Cram\'{e}r-Rao inequality. We show the resultant
TUR to give rise to the inequality of the product of the variance and entropy
production. We prove it to approach to the known overdamped result for large
viscosity limit. We present three examples to confirm our rigorous result.
