Damped oscillator consecutive amplitude ratio

[Uniquebum]

Homework Statement

Undamped oscillator's period $T_0 = 12s$. Damped oscillator's angular frequency $\omega_1 = \omega_0 * 97\%$ where $\omega_0$ is the angular frequency of the undamped oscillator's. What is the ratio of consecutive maximum amplitudes?

Homework Equations

Equation of damped oscillator's motion:
$x = e^{-\alpha t}A_0sin(\omega_1 t + \phi)$
where $\alpha = \frac{b}{2m}$ where $b =$damping constant.

The Attempt at a Solution

Firstly, were' talking about maximums so we can disregard the sin() function.
Calculating $\omega_1 = \omega_0 * 0.97 = \frac{2\pi}{T_0}0.97$.
Thus for the damped oscillator $T_1 = \frac{T_0}{0.97}$

Then we could write something as follows:
$\frac{x_0}{x_1} = \frac{e^{-\alpha t_0}A_0}{e^{-\alpha t_1}A_0}$
but we have no clue of alpha nor about x_0 and x_1... Any help appreciated.

 

[Stonebridge]

This is useful
http://en.wikipedia.org/wiki/Logarithmic_decrement

 

[Uniquebum]

I ended up using the formula

$\zeta = \sqrt{1-(\frac{\omega_1}{\omega_0})^2}$
And got approx 0.243 out of it. In my answer spreadsheet they claim the answer to be 0.21 however. Now I'm wondering whether i got it right or not... heh :) Thanks for the help either way.