About measurements in the presence of a high-frequency noise

About measurements in the presence of a high-frequency noise 

In order to find the displacement of the mass caused by this force, we introduce the function z t) as 

Taking the real part of this expression, we obtain 

As follows from Equation (3.169), if the frequency of free vibrations obeys the condition coo co, then the displacement. s(t) becomes very small s(t) oc l/oP. Taking into account this fact, it is possible to greatly reduce the influence of waves. Besides, a relatively strong attenuation allows one to decrease an effect of free vibrations caused by this force. 

---