31. Phase margin of a system is used to specify—
    

1. 1. relative stability
      

   
   
   

   2. absolute stability
      

   
   
   

   3. time response
      

   
   
   

   4. frequency response

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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32. The number of roots of the equation
    2s⁴ + s³ + 3s² + 5s + 7 = 0
    that lie in the right half of s plane is—
    

1. 1. zero
      

   
   
   

   2. one
      

   
   
   

   3. two
      

   
   
   

   4. three

   
   
   

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1. View Hint View Answer Discuss in Forum

   R.H.C. of the given C.E.
   2s⁴ + s³ + 3s² + 5s + 7 = 0
   s⁴ 2 3 7
   s³ 1 5
   s² – 7 7
   s¹ 6
   s⁰ 7
   since there are two sign changes, therefore, two roots in the right half plane.

   Correct Option: C

   R.H.C. of the given C.E.
   2s⁴ + s³ + 3s² + 5s + 7 = 0
   s⁴ 2 3 7
   s³ 1 5
   s² – 7 7
   s¹ 6
   s⁰ 7
   since there are two sign changes, therefore, two roots in the right half plane.

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33. The unit step response of a second order linear system with zero initial states is given by
    C (t) = 1 + 1.25 exp (– 6t) sin (8t – tan^–1 1.333); t ≥ 0
    The damping ratio and the undamped natural frequency of oscillation for the system are respectively—
    

1. 1. 0.6 and 10 rad/s
      

   
   
   

   2. 0.6 and 12.5 rad/s
      

   
   
   

   3. 0.8 and 10 rad/s
      

   
   
   

   4. 0.8 and 12.5 rad/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   From the expression for C (t), we get
   8 = ω_n√1 – ξ² …(i)
   and
   √1 – ξ²/ξ = 1.333 …(ii)
   solving these two equation, we get
   ω_n = 10 rad/sec, and ξ = 0.6

   Correct Option: A

   From the expression for C (t), we get
   8 = ω_n√1 – ξ² …(i)
   and
   √1 – ξ²/ξ = 1.333 …(ii)
   solving these two equation, we get
   ω_n = 10 rad/sec, and ξ = 0.6

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34. The Laplace transformation of f (t) is
    

    F(s) =	ω	=
    	s2 + ω2

    
    the final value of f(t) is—
    

1. 1. infinity
      

   
   
   

   2. zero
      

   
   
   

   3. one
      

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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35. If the gain of the open-loop system is doubled, the gain margin—
    

1. 1. is not affected
      

   
   
   

   2. gets double
      

   
   
   

   3. becomes half
      

   
   
   

   4. becomes one-fourth

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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