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Transmissibility vs frequency ratio for different amount of damping.
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These curves can be divided into two ranges:

First from $(w/w_n) = 0$ to $(w/w_n) = \sqrt{2}$

And second from $(w/w_n) = \sqrt{2}$ to $(w/w_n) \rightarrow \infty$

In the first range, greater amount of damping gives greater transmissibility, which is always greater then unity.

In the second range, greater amount of damping gives greater transmissibility, which is always less then unity.

This means that damping is favorable in the first range and unfavorable in the second range.

In order to have low value of transmissibility, the operating range is generally kept far away in the second range. Under these conditions, zero damping will be ideally suitable as this would give extremely low value of transmissibility.

But since the system has pass through the resonance in reaching the operating point and zero damping will give very high transmissibility, some amount of damping is generally incorporated in the system of the cast of little higher transmissibility at the operating point.

Some systems operating in the first range at very ow values of $w/w_n$ for these systems higher the damping, lesser the transmissibility.

Isolation efficiency:

$\eta iso \ = \ \frac{force \ by \ which \ it \ is \ isolated}{impressed \ force}$

$\eta iso = 1 \ – \ T_r$

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