INTRODUCTION TO LAPLACE TRANSFORMS 631
K
- (a) 5e^3 t(b) 2e−^2 t
[
(a)
5
s− 3
(b)
2
s+ 2
]
- (a) 4 sin 3t(b) 3 cos 2t
[
(a)
12
s^2 + 9
(b)
3 s
s^2 + 4
]
- (a) 7 cosh 2x(b)
1
3
sinh 3t
[
(a)
7 s
s^2 − 4
(b)
1
s^2 − 9
]
- (a) 2 cos^2 t (b) 3 sin^22 x
[
(a)
2(s^2 +2)
s(s^2 +4)
(b)
24
s(s^2 +16)
]
- (a) cosh^2 t(b) 2 sinh^22 θ
[
(a)
s^2 − 2
s(s^2 −4)
(b)
16
s(s^2 −16)
]
- 4 sin(at+b), whereaandbare constants
[
4
s^2 +a^2
(acosb+ssinb)
]
- 3 cos(ωt−α), whereωandαare constants
[
3
s^2 +ω^2
(scosα+ωsinα)
]
- Show thatL(cos^23 t−sin^23 t)=
s
s^2 + 36
