enjoyingprocess88991 enjoyingprocess88991
  • 07-08-2019
  • Engineering
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A second onder system with damping ratio of 0.4 on a unit-step input will produce a maximum overshoot of a bout (A) 25% (B) 45% (C) 65% (D) 85% (E) none of above

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aristeus aristeus
  • 12-08-2019

Answer:

(a) 25%

Explanation:

It is given that damping ratio [tex]\zeta =0.4[/tex]

The maximum peak overshoot [tex]M_P[/tex]  is given by [tex]M_P=e^\frac{-\pi \zeta }{\sqrt{1-\zeta ^2}}[/tex]

So [tex]M_P=e^\frac{-3.14\times 0.4}{\sqrt{1-0.4^2}}=0.2538=25.28[/tex] % which is nearly equal to the 25 % so the option (a) will be the correct option as in option (a) it is given that maximum peak overshoot is 25%

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