Transmissivity versus frequency ratio curve for various values of damping factor (ξ) is shown in figure. Which of y the following is correct?

Explanation:

Vibration Isolation: 

• The purpose of vibration isolation is to control the transmission of the vibration to the base upon which the machines are installed.
• It is done by mounting the machines on the spring, dampers, or other vibration isolation material. 
  • Force transmissibility is defined as the ratio of force transmitted to the foundation that impressed on the system.
  • For a viscous damped system with impressed force F0 and transmitted force FT, transmissibility is given as 

\(\frac{{{F_T}}}{{{F_0}}} = {\rm{\;Transmissibility\;}} = \frac{{\sqrt {1 + {{\left( {2\xi r} \right)}^2}} }}{{\sqrt {{{\left( {1 - {r^2}} \right)}^2} + {{\left( {2\xi r} \right)}^2}} }}\)

Where, ω = speed of the exciting source, radIs, ωn = natural frequency of system, radIs, ζ = damping ratio

The transmissibility curve for different values of the damping ratio is shown below

Conclusions:

• Independent of the value of the damping ratio, the transmissibility of the mechanical system tends to zero as the value of the frequency ratio is above √2. The section beyond the frequency ratio \(\sqrt2\)  is known as the Isolation part of the transmissibility curve i.e., For effective vibration isolation, the frequency ratio \(\frac{\omega_n}{\omega}\) must be less than \(\frac{1}{\sqrt2}\)
• If the frequency ratio (ω/ωn) is less than\(\sqrt2\) then the transmitted force is always greater than the exciting force.
• If the frequency ratio (ω/ωn) is equal to \(\sqrt2\) then the transmitted force is equal to the exciting force.