(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

Equation of damped oscillator's motion:

[itex]x = e^{-\alpha t}A_0sin(\omega_1 t + \phi)[/itex]

where [itex]\alpha = \frac{b}{2m}[/itex] where [itex]b = [/itex]damping constant.

3. The attempt at a solution

Firstly, were' talking about maximums so we can disregard the sin() function.

Calculating [itex]\omega_1 = \omega_0 * 0.97 = \frac{2\pi}{T_0}0.97[/itex].

Thus for the damped oscillator [itex]T_1 = \frac{T_0}{0.97}[/itex]

Then we could write something as follows:

[itex]\frac{x_0}{x_1} = \frac{e^{-\alpha t_0}A_0}{e^{-\alpha t_1}A_0}[/itex]

but we have no clue of alpha nor about x_0 and x_1... Any help appreciated.

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# Damped oscillator consecutive amplitude ratio

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