082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

110 Chapter 2 Engineering functions
Example2.25 Sketch the following functions:
(a) f =u(t−3)
(c) f =u(t−1)−u(t−3)
(e) f =e t u(t)
(b) f =u(t−1)
(d) f =u(t−3)−u(t−1)
Solution (a) See Figure 2.51. (b) See Figure 2.52.
(c) See Figure 2.53. (d) See Figure 2.54.
(e) See Figure 2.55.
f
1
f
1
Figure2.51
Thefunction: f =u(t −3).
3 t
Figure2.52
The function: f =u(t −1).
1
t
f
1
f
f
Figure2.53
Thefunction:
f =u(t−1)−u(t−3).
1
3
t
–1
1 3
Figure2.54
Thefunction:
f =u(t−3)−u(t−1).
t
1
Figure2.55
Thefunction: f = e t u(t).
t
EXERCISES2.4.8
1 Sketch the followingfunctions:
(a) f(t) =u(t −1)
(b) f(t) =u(t +1)
(c) f(t)=u(t−2)−u(t−6)
(d) f(t) =3u(t −1)
(e) f(t)=u(t+1)−u(t−1)
(f) f(t)=u(t−1)−u(t+1)
(g) f(t) =u(t +1)−2u(t −1)
(h) f(t) =2u(t +1)−u(t −1)
(i) f(t) =3u(t −1)−2u(t −2)
2 Aramp function, f (t),is defined by
{ 2t t0
f(t)=
0 t<0
Sketch the following for −1 t 3:
(a) f(t)
(b) u(t)f(t)
(c) u(t −1)f(t)
(d) u(t −1)f(t)−u(t −2)f(t)
Solutions
2 SeeFigureS.5.