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.