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Uniquebum
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Homework Statement
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?
Homework 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.
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.