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I know that the step response of a second order underdamped system is :

y(t) = 1 – (e^(-ζωn*t) / sin(θ))*sin(ωd*t + θ)

Where sin(θ)= sqrt(1-ζ^2) , ωd = sqrt(ωn^2 – ωn^2 * ζ^2 )

my question is: I can see on the simulation ωd and I can calculate it ,

but I want also to see the phase shift angle θ

I know already that θ= asin(sqrt(1-ζ^2) ) , but this is analytical, can I see and measure it on the graph?

thanks

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# Understanding the physical meaning of phase shift in underdamped systems

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