Chapter 19.4, Problem 19.113P

To determine

Show that when the angular velocity of the motor is $\left({\omega }_f\right)$ the amplitude $\left(x_m\right)$ of the motion of the motor.

$x_m=\frac{r\left(\frac{m}{M}\right){\left(\frac{{\omega }_f}{{\omega }_n}\right)}^2}{1-{\left(\frac{{\omega }_f}{{\omega }_n}\right)}^2}$