Solution 2.9.2.2
f(t)=e
;at
[1(t;T);1(t ;2T)]
Then
F(s) = Lfe
;at
[1(t;T)g;1(t; 2T)]g
= Lfe
;at
1(t;T)g;Lfe
;at
1(t ;2T)g
= Lfe
;aT
e
;a(t;T)
1(t; T)g;Lfe
;2Ta
e
;a(t;2T)
1(t; 2T)g
=
e
;aT
e
;Ts
s + a
;
e
;2aT
e
;2Ts
s + a
=
e
;aT
e
;Ts
;e
;2aT
e
;2Ts
s + a
Check:
F(s) =
Z
2
T
Te
;at
e
;st
dt
=
;1
s + a
h
e
;(s+a)t
i
2T
T
=
;1
s + a
h
e
;(a+s)2T
; e
;(s+a)2T
i
=
e
;aT
e
;sT
;e
;2aT
e
;2Ts
s + a
1