76. The impulse response of an initially relaxed linear system is e ^{– 2t} u(t). To produce a response of te ^{– 2t}u(t), the input must be equal to
    

1. 1. 2 e ^{– t} u(t)

   
   
   

   2. 1	e – 2t u(t)
      2

   
   
   

   3. e ^{– 2t} u(t)

   
   
   

   4. e ^{– t} u(t)

   
   
   

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1. View Hint View Answer Discuss in Forum

   H(s) =	1
   	s + 2

   
   

   Y(s) =	1	, X(s) =	Y(s)	=	1
   	(s + 2)2		H(s)		s + 2

   
   and u(t) = e ^{– 2t} u(t)
   

   Correct Option: C

   H(s) =	1
   	s + 2

   
   

   Y(s) =	1	, X(s) =	Y(s)	=	1
   	(s + 2)2		H(s)		s + 2

   
   and u(t) = e ^{– 2t} u(t)
   

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77. The close-loop transfer function of a control system is given by
    

    	C(s)	=	1
    	R(s)		1 + s

    
    For the input r(t) = sin t, the steady state value of c(t) is equal to

1. 1. 	1	cos t
      	√2

   
   
   

   2. 1

   
   
   

   3. 	1	sin t
      	√2

   
   
   

   4. 	1	sin		t -	π
      	√2				4

   
   
   

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1. View Hint View Answer Discuss in Forum

   	C(s)	=	1
   	R(s)		1 + s

   
   

   ⇒	C(jω)	=	1
   	R(jω)		1 + jω

   
   
   

   ∴ Steady state value at c(t) =	1	sin		t -	π
   	√2				4

   
   

   Correct Option: D

   	C(s)	=	1
   	R(s)		1 + s

   
   

   ⇒	C(jω)	=	1
   	R(jω)		1 + jω

   
   
   

   ∴ Steady state value at c(t) =	1	sin		t -	π
   	√2				4

   
   

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78. For a feedback control system of type 2, the steady state error for a ramp input is
    

1. 1. infinite

   
   
   

   2. constant

   
   
   

   3. zero

   
   
   

   4. indeterminate

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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79. In the derivative error compensation, damping
    

1. 1. decreases and settling time decreases

   
   
   

   2. increases and settling time increases

   
   
   

   3. decreases and settling time increases

   
   
   

   4. increases and settling time decreases

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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80. For the unity feedback system shown below, the steady state error, when the input is
    

    R =	3	-	1	+	1	, would be
    	s		s2		2s3

    
    

1. 1. 1

      4

      
      

   
   
   

   2. 0
      

   
   
   

   3. ∞
      

   
   
   

   4. 1

      2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Steady state error,
   

   Correct Option: A

   Steady state error,
   

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