Acceleration amplitude of a damped harmonic oscillator

[TheBigDig]

Homework Statement

The acceleration amplitude of a damped harmonic oscillator is given by
$$A_{acc}(\omega) = \frac{QF_o}{m} \frac{\omega}{\omega _o} \sqrt{\it{R}(\omega)}$$
Show that as $\lim_{\omega\to\infty}, A_{acc}(\omega) = \frac{F_o}{m}$

Homework Equations

$$\it{R}(\omega) = \frac{(\gamma \omega)^2}{(\omega _o ^2 - \omega^2)^2 +(\gamma \omega)^2} $$
$$ Q = \frac{\omega _o}{\gamma}$$

The Attempt at a Solution

From substituting in the above equations into the formula and cancelling off, I've gotten this far
$$\frac{F_o}{m} \frac{\omega ^2}{\sqrt{(\omega _o ^2 - \omega^2)^2 +(\gamma \omega)^2}}$$
I'm fairly certain I haven't made any mistakes in my cancelling off. I don't see how the equation will tend to $\frac{F_o}{m}$ as surely $\frac{\omega ^2}{\sqrt{(\omega _o ^2 - \omega^2)^2 +(\gamma \omega)^2}}$ will go to zero.

 

[kuruman]

Look at the denominator. What does it become when $\omega$ becomes very large? In other words, what is its $\omega$ dependence?