Page 25 - LAPLACE TRANSFORM
P. 25
A B
-2t
2 3t
4) f(t) = 5 t e + 6 e sin 4t
i) A: ʆ {5 t } = 5 [ ! ] (refer to table)
2
( ) +1
2!
= 5 [ ]
( ) 2+1
= 10
( ) 3
2 3t
ʆ {5 t e } = 10 change s to s= (s−3)
( ) 3
=
( − )
ii) B: ʆ {6 sin 4t} = 6 [ ]
2
+ 2
= 6 [ 4 ]
2
+4 2
= 24
2
+4 2
-2t
ʆ {6 sin 4t e } = 24 change s to s= (s+2)
2
+4 2
= 24
2
( +2) +4 2
=
( + ) +
2 3t
-2t
ʆ {f(t)} = ʆ {5 t e + 6 e sin 4t}
= +
( − ) ( + ) +
19
