The Vibration Transmission Loss of** the one degree of freedom system ** is calculated by assuming a damped mass-spring system. The ratio between the exciting force and the transmitted force is calculated with :

$$ T = \left| \frac{F'}{F} \right| = \left[ \frac{1 + \left( \frac{2 \xi \omega}{\omega_0} \right)^2}{\left( 1 - \left( \frac{\omega}{\omega_0} \right)^2 \right)^2 + \left( 2 \xi \frac{\omega}{\omega_0} \right)^2} \right]^\frac{1}{2} $$
The resonance frequency in Hz is calculated taking into account a damped system:

$$ f_p = f_0 \sqrt{1 - 2\xi^2} $$
with \( f_0 \) the resonance frequency of undamped system inHz

The calculation of the two resonant frequencies is done following

See also my article about the different strategies for good vibration reduction.