PROBLEMS 185

4 Ω

(^4) 10 V
5 H
20 V
iL(t)
S
t = 0
4 Ω

• −


• 
  

  −
  201 F vC(t)

  
  


• 
  

  −
  Figure P3.2.16
  f(t)
  Step functions
  t
  5
  01
  10
  15
  20
  25
  2 3 4 5 6 7 8 9
  Figure P3.2.17
  v, V
  t, s
  1 2
  10
  − 10
  Figure P3.2.18
  3.3.4Determine the inverse Laplace transform of each
  of the following functions.
  (a)
  6 (s+ 3 )
  s^2 + 2 s+ 10
  (b)
  s+ 2
  (s+ 1 )(s+ 3 )(s+ 4 )
  (c)
  8 (s+ 1 )
  s(s^2 + 2 s+ 2 )
  (d)
  s^2 + 4 s+ 5
  s^2 + 3 s+ 2
  (e)
  2 (s+ 2 )
  s(s+ 1 )^3
  (f)
  s+ 1
  s^3 + 4 s^2 + 3 s
  (g)
  10 (s^2 + 3 s+ 2 )
  3 (s^2 + 2 s+ 2 )
  (h)
  (s+ 1 )(s+ 2 )
  s^2 (s^2 + 2 s+ 2 )
  (i)
  4 s
  (s^2 + 4 )(s+ 2 )
  (j)
  4 s
  [
  (
  s+ 2 )^2 + 4
  ] 2
  3.3.5Solve the following differential equations (along
  with the conditions) fort≥0.
  (a)
  d^2 v
  dt^2

  
  


• 5
  dv
  dt


• 
  

  4 v= 10 u(t);v
  (
  0 +
  )

  
  

  dv
  ( dt
  0 +
  )
  = 0