
The transient component is
v
c
(t)
tr
¼ [v
c
(0) KE
0
]e
t=RC
, t 0
¼ [3 (1)(12)]e
t=62510
6
¼9e
t=62510
6
and the steady-state component is
v
c
(1) ¼ KE ¼ 1
V
V
(12 V) ¼ 12 V
Graphs of the steady-state, transient, and complete responses are shown in Figure 2.3.
Note that the transient response has decayed to essentially zero after five time constants
(5 625 10
6
¼3.125 10
3
) have elapsed.
EXERCISES
2.1 The tank shown in Figure 2.2 has a constant cross-sectional area A and fluid resistance R.
(a) Find expressions for the time constant t and steady-state gain K of the tank in terms of the
physical parameters A and R.
(b) The empty tank is subject to a constant ...