Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of three systems?

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Solution

The correct option is C
Peak overshoot depends on $ξ$ as
$M_{P} = e^{- ξ π \sqrt{1 - ξ^{2}}}$
$w h e r e ξ = c o s θ$
where $θ$ is the angle made by pole from negative real axis.
To make $M_{P}$ same, $θ$ should be the same.

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Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of three systems?

The correct option is C Peak overshoot depends on ξ as MP=e−ξπ√1−ξ2 where ξ=cos θ where θ is the angle made by pole from negative real axis. To make MP same, θ should be the same.

The correct option is C
Peak overshoot depends on $ξ$ as
$M_{P} = e^{- ξ π \sqrt{1 - ξ^{2}}}$
$w h e r e ξ = c o s θ$
where $θ$ is the angle made by pole from negative real axis.
To make $M_{P}$ same, $θ$ should be the same.