The governing EOM of the two DOF system may be written as

	(19.1)
	(19.2)

Using

from Equation 19.2 we get

or

or

(19.3)

Similarly, from Equation 19.1, we get

or,

or

Thus, when the hydraulic actuator is switched on the active displacement of the primary mass may be written as:

When the hydraulic system is switched off, the passive displacement of the primary mass may be written as

The ratio of active and passive displacement of the primary mass brings out the efficiency of the new system. Therefore,

For a simple case, use

As a test case,

                                 for         
                       and    for         

From these expressions, you can check that the negetive feedback system with works better for a wider frequency range.