96. Equivalent of the block diagram in the figure is
    
    

1. 1. 
      

   
   
   

   2. 
      

   
   
   

   3. 
      

   
   
   

   4. 
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: D

   NA

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97. A control system whose step response is
    – 0.5 (1 + e^{– 2t})
    is cascaded to another control block whose impulse response is e ^{– t}. The transfer function of the cascaded combination is

1. 1. 	1
      	(s + 1)(s + 2)

   
   
   

   2. 	1
      	s(s + 2)

   
   
   

   3. 	1
      	(s + 2)

   
   
   

   4. 	0.5
      	(s + 1)(s + 2)

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   C1(s) = 0.5			1	+	1			=	0.5 × 2(s + 1)
   			s		s + 2				s(s + 2)

   
   

   ∴ G1 (s) =	C(s)	=		(s + 1)		=	(s + 1)
   				s(s + 2)
   	R(s)			1			(s + 2)
   				s

   
   

   H2(s) =	1
   	s + 1

   
   

   ∴ H(s) = H1(s) H2(s) =	1
   	s + 2

   Correct Option: C

   C1(s) = 0.5			1	+	1			=	0.5 × 2(s + 1)
   			s		s + 2				s(s + 2)

   
   

   ∴ G1 (s) =	C(s)	=		(s + 1)		=	(s + 1)
   				s(s + 2)
   	R(s)			1			(s + 2)
   				s

   
   

   H2(s) =	1
   	s + 1

   
   

   ∴ H(s) = H1(s) H2(s) =	1
   	s + 2

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98. In the following block diagram G1 =	10	; G2 =	10	; H1 = s + 3 and H2 = 1.
    	s		(s + 1)

    
    The overall transfer function C/R is given by
    

1. 1. 	10
      	11s2 + 31s + 10

   
   
   

   2. 	100
      	11s2 + 31s + 100

   
   
   

   3. 	100
      	11s2 + 31s + 10

   
   
   

   4. 	100
      	11s2 + 31s

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Successive block diagram reduction can be
   
   

   	C(s)	=		G1 G2		=	G1 G2
   				1 + G2 H1
   	R(s)		1 +	G1 G2 H2			1 + G2H1 + G1 G2 H2
   				1 + G2 H1

   
   
   

   =	100
   	11s2 + 31s + 100

   
   

   Correct Option: B

   Successive block diagram reduction can be
   
   

   	C(s)	=		G1 G2		=	G1 G2
   				1 + G2 H1
   	R(s)		1 +	G1 G2 H2			1 + G2H1 + G1 G2 H2
   				1 + G2 H1

   
   
   

   =	100
   	11s2 + 31s + 100

   
   

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99. For block diagram shown in the figure,	C(s)	is given by
    	R(s)

    
    

1. 1. 	G1 G2 G3
      	1 + H2G2G3 + H1G1G2

   
   
   

   2. 	G1 G2 G3
      	1 + G1G2G3H1H2

   
   
   

   3. 	G1 G2 G3
      	1 + G1G2G3H1 + G1G2G3H2

   
   
   

   4. 	G1 G2 G3
      	1 + G1G2G3H1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let output of summer is K (s). Then
   

   K(s) =	C(s)
   	G2 G3

   
   

   ∴	C(s)	= G1		R(s) -	C(s)H1		- C(s)H2
   	G2 G3				G3

   
   ⇒ C(s) [1 + H₁ G₁ G₂ + H₂ G₂ G₃ ] = G₁ G₂ G₃ R (s)
   

   ⇒	C(s)	=	G1 G2 G3
   	R(s)		1 + H2G2G3 + H1G1G2

   Correct Option: A

   Let output of summer is K (s). Then
   

   K(s) =	C(s)
   	G2 G3

   
   

   ∴	C(s)	= G1		R(s) -	C(s)H1		- C(s)H2
   	G2 G3				G3

   
   ⇒ C(s) [1 + H₁ G₁ G₂ + H₂ G₂ G₃ ] = G₁ G₂ G₃ R (s)
   

   ⇒	C(s)	=	G1 G2 G3
   	R(s)		1 + H2G2G3 + H1G1G2

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100. The response c(t) of a system to an input r(t) is given by the following differential equation :
     

     	d2c(t)	+ 3	dc(t)	+ 5c(t) = 5 r(t)
     	dt2		dt

     
     The transfer function of the system is given by

1. 1. G(s) =	5
      	s2 + 3s + 5

   
   
   

   2. G(s) =	5
      	s2 + 3s + s

   
   
   

   3. G(s) =	3s
      	s2 + 3s + 5

   
   
   

   4. G(s) =	s + 3
      	s2 + 3s + 5

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given equation is,
   

   	d2c(t)	+ 3	dc(t)	+ 5 c(t) = 5 r(t)
   	dt2		dt

   
   Taking Laplace transform, we get
   (s² + 3s + 5) C (s) = 5 R (s)
   

   ∴	C(s)	=	1
   	R(s)		s2 + 3s + 5

   Correct Option: A

   Given equation is,
   

   	d2c(t)	+ 3	dc(t)	+ 5 c(t) = 5 r(t)
   	dt2		dt

   
   Taking Laplace transform, we get
   (s² + 3s + 5) C (s) = 5 R (s)
   

   ∴	C(s)	=	1
   	R(s)		s2 + 3s + 5

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