
3.2.2 Solution of the second-order circuit zero-state response
According to the solving principle of the second-order differential equation, the solution for zero
state of second-order circuit has two parts, they are compulsory component of zero state u
c1
and
free component of zero state u
c2
, respectively. u
c1
is obtained by the phasor method:
Where u
c1
is the phasor of u
c1
, Z
C
=
1
jωC
, Z
L
=jωL,
˙
U
s
=U
m
∠57
◦
, the solution of formula (13) is
The form of zero-state free component is as follows: u
c2
=e
−δt
(B
1
cos ω
z
t + B
2
sin ω
z
t)
Because u
c
=u
c1
+ u
c2
When formula (14) are substituted into formula (15), we can get
B
1
=260.93
B
2
=155.93
So the zero-state response of