Question

A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of the isolation system is equal to 0.5, the transmissibility ratio of isolation is

• A. $\frac{1}{2}$
• B. $\frac{3}{4}$
• C. $\frac{4}{3}$
• D. 2

Answer 1

The correct option is C $\frac{4}{3}$

Given r = 0.5
Due to isolation

${\xi }_s=0$
Transmissibility ratio,

$TR=\frac{\sqrt{1+(2\xi r{)}^2}}{\sqrt{(1-r^2{)}^2+(2\xi r{)}^2}}$

$=\frac{1}{\sqrt{(1-({0.5}^2){)}^2}}=\frac{1}{1-0.25}=\frac{4}{3}$