Second Order System

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A second order system exibhits 100% overshoot.It's damping coefficient is

(a)0

(b)1

(c)&lt 1

(d)&gt 1

Answer is ( a )

Concept

Explanation:For a second order system , Peak OverShoot is $M_p = 100$ %

$M_p = e^{\frac{-\zeta}{\sqrt{1-\zeta^2}}}$

$e^{\frac{-\zeta}{\sqrt{1-\zeta^2}}} = 100% = 1$

Taking Logarithm on both sides,$\frac{-\zeta}{\sqrt{1-\zeta^2}} = ln(1) = 0$

This implies, $\zeta = 0$

This indicates no damping