Page 55 - LAPLACE TRANSFORM

0 = A + B ............................... (1)
− A = B,
B = −A = −

5 = 41A + 2C ......................... (3)
3
2
2C = 5 − 41A = 5 − 41( ) =
25 25

C = 2 =
2 (25)

f(t) = + +
2
+2 s +10 +41

1
3
3 (− ) + ( )
= 25 + 25 25
2
+2 s +10 +41

3 1 ( −3 +1 )
= 25 + 25
2
+2 s +10 +41

1 −3 +1
= { } + { }
2
+2 (s+5) +4 2
(-3s -15) + 16 = -3s + 1

3 -2t 1 −3( +5) + 16
= e + { }
2
25 25 (s+5) +4 2

3 1 −3( +5) 16
-2t
= e + { + }
2
2
25 25 (s+5) +4 2 (s+5) +4 2

1
-2t
= 3 e + { −3( ( +5) ) + 4( 4 ) }
2
2
25 25 (s+5) +4 2 (s+5) +4 2

3
1
-5t
-2t
-5t
= e + { −3e 4 + 4e Sin 4t }
25 25

-5t
-2t
-5t
= e − e + e Sin 4t

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