81. A second order system with no zeros has its poles located at – 3 + j4 and – 3 – j4 in the s-plane. The undamped natural frequency and the damping factor of the system are respectively—
    

1. 1. 4 rad/sec and 0.75
      

   
   
   

   2. 3 rad/sec and 0.60
      

   
   
   

   3. 5 rad/sec and 0.80
      

   
   
   

   4. 5 rad/sec and 0.60

   
   
   

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   NA

   Correct Option: A

   NA

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82. The output of a linear system for a unit step input is given by t 2e–t. The transfer function is given by—
    

1. 1. s/(s + 1)³
      

   
   
   

   2. 2s/(s + 1)³
      

   
   
   

   3. 1/s² (s + 1)
      

   
   
   

   4. 2.s(s + 1)²

   
   
   

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   NA

   Correct Option: A

   NA

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83. Signal flow graph is used to obtain the—
    

1. 1. stability of the system
      

   
   
   

   2. transfer function of a system
      

   
   
   

   3. controllability of a system
      

   
   
   

   4. observability of a system

   
   
   

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   Signal flow graph is used to obtain the transfer function of a system.

   Correct Option: B

   Signal flow graph is used to obtain the transfer function of a system.

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84. Which of the following figure(s) represent valid root loci in the s-plane for positive K? Assume that the system has a transfer function with real coefficients—

1. 1. Fig:- A
      

   
   
   

   2. Fig:- B
      

   
   
   

   3. Fig:- C
      

   
   
   

   4. Fig:- D
      

   
   
   

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   Only (A) is valid root loci since in option (B), (C) and (D), the root loci lies to the left half of s-plane having an even number of zeros and poles, not odd. Hence alternative (A) is the correct choice.

   Correct Option: A

   Only (A) is valid root loci since in option (B), (C) and (D), the root loci lies to the left half of s-plane having an even number of zeros and poles, not odd. Hence alternative (A) is the correct choice.

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85. A second order system is given as
    

    G(s) =	K
    	(1 + τ1s) (1 + τ2s)

    
    If the gain K is increased, then the phase margin—
    

1. 1. gets increased
      

   
   
   

   2. gets decreased
      

   
   
   

   3. is unaffected
      

   
   
   

   4. gets decreased and becomes stable

   
   
   

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   NA

   Correct Option: B

   NA

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