Damped oscillator- graphical interpretation

[rsaad]

Hi!
The damped oscillator equation is as follows:
x(t)= A exp(γt/2) cos(ωt)

where ω= √( (w0)^2 + (γ^2)/4 )

I have attached a graph of a damped oscillator.
The question is if I use graph to measure angular frequency, will it be w0 or ω?

It should be w0 because if I put γ=0, I should be getting the normal undamped system. The enveloped curve would disappear since exp(γt/2) is 1. BUT then where is ω on the graph!

 

[PhysicoRaj]

How can u expect ω in an x-t graph? You will have to calculate.

 

[rsaad]

of course I know that. Let m rephrase. The time T between successive maxima is constant. So I consider the complete oscillations, k, for a given time, t. To get angular frequency, W= k* 2pi/t
The question is, what is this this W? is it w0 or is it the angular frequency ω of the damped oscillator

 

[andrien]

it is the angular frequency of damped oscillator.

 

[Philip Wood]

The answer to your question is ω. Peaks in the damped sinusoid e^{-kx} cos(\omega t)occur a little before the peaks in the pure sinusoid cos(\omega t), but by the same amount each time, so the time between peaks is the same as that between the peaks in cos(\omega t).

 

[AlephZero]

e^{-kx} cos(\omega t)[/itex]occur a little before the peaks in the pure sinusoid cos(\omega t), but by the same amount each time, so the time between peaks is the same as that between the peaks in cos(\omega t).

An easier way to see the anwer is $\omega$ is to think about the times when x(t) = 0. They are the roots of $\cos \omega t = 0$.

 

[Philip Wood]

AlephZero. Agree, but thought rsaad (in post 3) was worried about maxima.