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GATE 2014 EC (EC2) – Question 15

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

The characteristic equation of $d^2y/dx^2+2\alpha\,dy/dx+y=0$ has equal roots. Find possible $\alpha$.

  1. $\pm1$
  2. 0,0
  3. $\pm j$
  4. $\pm1/2$

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Show answer and explanation

Correct answer: (A) $\pm1$

Explanation

The equation y″+2αy′+y=0 has characteristic polynomial r²+2αr+1. Equal roots require discriminant(2α)²−4=0, or α²=1. Therefore **α=±1,A**. Both signs give repeated roots, although only positiveα corresponds to ordinary positive damping.