71. The response of an initially relaxed linear circuit to a signal V_s is e^{– 2t}u(t). If the signal is changed to (V_s + 2(dV_s/dt), then response will be

1. 1. – 4e^{– 2t} u(t)

   
   
   

   2. – 3e^{– 2t} u(t)

   
   
   

   3. 4e^{– 2t} u(t)

   
   
   

   4. 5e^{– 2t} 4(t)

   
   
   

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1. View Hint View Answer Discuss in Forum

   When the excitation of alinear system is differential, the output also is the differentiation of previous output
   ∴ Response = e^{– 2t} u(t) + 2 d/dt[e^2t u(t)] = – 3e^{– 2t} u(t)

   Correct Option: B

   When the excitation of alinear system is differential, the output also is the differentiation of previous output
   ∴ Response = e^{– 2t} u(t) + 2 d/dt[e^2t u(t)] = – 3e^{– 2t} u(t)

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72. If system is initially at rest, the response to a unit step u(t) is given by 1/2 (1 – e^{– 2t}) The response to a signal u(t) + 2δ (t) is given by

1. 1. 1	+	3	e-2t
      2		2

   
   
   

   2. 1 + e^{– 2t}

   
   
   

   3. 1 + 3 e^{– 2t}

   
   
   

   4. 1	+	1	e-2t
      2		2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here C(t) =	1	(1 - e-2t, R(s) =	1
   	2		s

   
   

   i.e C(s) =	1		1	-	1		=	1
   	2		s		s + 2			s(s + 2)

   
   

   H(s) =	L(s)
   	R(s)

   
   

   u(s) =	1
   	s + 2

   
   

   Now for R'(s) =	1	+ 2
   	s

   
   

   ⇒ C'(s) =

   1

   ×

   1

   + 2

   =

   2s + 1

   =

   A

   +

   B

   (s + 2)

   s

   s(s + 2)

   s

   s + 2

   
   

   Correct Option: A

   Here C(t) =	1	(1 - e-2t, R(s) =	1
   	2		s

   
   

   i.e C(s) =	1		1	-	1		=	1
   	2		s		s + 2			s(s + 2)

   
   

   H(s) =	L(s)
   	R(s)

   
   

   u(s) =	1
   	s + 2

   
   

   Now for R'(s) =	1	+ 2
   	s

   
   

   ⇒ C'(s) =

   1

   ×

   1

   + 2

   =

   2s + 1

   =

   A

   +

   B

   (s + 2)

   s

   s(s + 2)

   s

   s + 2

   
   

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73. The Laplace transform of sinh at is

1. 1. a
      s² - a²

   
   
   

   2. s
      s² - a²

   
   
   

   3. s
      s² + a²

   
   
   

   4. a
      s² + a²

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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74. The Laplace transform of f(t) = t is given by

1. 1. 1
      s²

   
   
   

   2. 1
      s

   
   
   

   3. 2
      s³

   
   
   

   4. s

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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75. Laplace transform of t sin at is

1. 1. 2as
      (s² + a²)²

   
   
   

   2. 2a
      (s² + a²)²

   
   
   

   3. 2s
      (s² + a²)²

   
   
   

   4. a
      (s² + a²)²

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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