Chapter 4.P1, Problem 3P

Plot the graphs of $T_R$ versus the dimensionless ratio $\omega /{\omega }_0$ for $\zeta =0.1,0.5,1.2$. For what values of $\omega /{\omega }_0$ is $T_R=1$ ? Explain why the graphs imply that it is desirable that the mountings have a low natural frequency in order to isolate the vibration source from the equipment platform, and that using low-stiffness isolators is one way to achieve this.

$T_R=\frac{\sqrt{1+{\left(2\zeta \frac{\omega }{{\omega }_0}\right)}^2}}{\sqrt{{\left[1-{\left(\frac{\omega }{{\omega }_0}\right)}^2\right]}^2+{\left[2\zeta \frac{\omega }{{\omega }_0}\right]}^2}}$