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Vibration Transmission Calculation

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

For the double suspension, the system is composed of 2 masses and 2 springs connected to a rigid ground. The calculation of the Transmissibility come from Bies - Engineering Noise Control Theory and Practice $$ T = \frac{(k_1 + j\omega C_1)(k_2 + j\omega C_2)}{(k_1 + k_2 - \omega^2 m_1 + j\omega C_1)(k_2 - \omega^2 m_2 + j\omega C_2) - (k_2 + j\omega C_2)^2} $$ with indice 1, mass, stiffness and damping connected to the ground and with indice 2, mass, stiffness and damping above the system 1. double suspension system for vibration calculation
The calculation of the two resonant frequencies is done following Harris' Shock and Vibration Handbook - Fifth Edition P1.10

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