# Passive Vibration Isolation

The classical approach of passive isolation is based on the phenomenon of inertia. In principle a passive isolation configuration is assembled by a mass M supported by a spring (spring constant c) and a damper (damping coefficient d).

The excitation (building vibration at the floor) is defined by

with as the excitation amplitude and as the circular excitation frequency. The system response is given by

Formulating the equation of motion

applying the defined excitation and response and using some algebraic conversions the so-called transmission can be specified as

In the resonance of the passive system the circular excitation frequency equals the circular eigenfrequency and the transmission gets

Therefore in the case of resonance the transmission is limited by the viscous damping. Nevertheless even by the assumption of infinite viscous damping the transmission can not be reduced below the value of 1. On the other side high viscous damping leads to less isolation for excitation frequencies above the resonance since the value of the numerator is increasing with the frequency. In practice the viscous damping as to be adjusted to achieve acceptable amplification within the resonance and desired isolation for higher frequencies.