Since all the energy starts out the capacitor
684  C H A P T E R 


i n  s e c o n d  o r d e r 

2. Since there is no drive, and since there is a dissipative element in the circuit, the final value of the capacitor voltage is given by
vC(∞) = 0 V.
4.  

α =  1  
2RC  
ωo =  1 √LC 

and the ringing frequency is
5.  ωd =  

Q =ωo 2α 
The form of vC(t) can now be plotted as shown in Figure 12.59.


vC(V)  1.0  VCM  2 

R1  C H A P T E R 

685  

0.5  v1  v2  
0.0  
0.5  VCM  C1  
R2  C2  
1.0  3  4  


t (ms) 
FIGURE 12.59 Sketching the form of vC for a parallel RLC circuit driven by an impulse current input.
C  dv1(t)  1  v(t)1 



1  dt  + R1 

C  dv2(t)  1  v(t)1  

2  dt  + R2 


v2(t) = R3C1  dv1(t)  +  �1R3  �  

dt  + R1  �  

1  +  1 



+  R2C2  R3C1  
1  +  
+  R1R3C1C2 