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 Step-Response Series 
  RLC Circuits (2)
 
 
 The solution of the
 equation should have two components:
 the transient
 response vt(t) & the steady-state response vss(t):
  
 
  
  
   
   
   
   
   
   
   
   
   
   
   
   
  
  
  
 
  
 
  
  
  
  
  
 
  
  
  
 
  
  
  
 
 ·The transient response vt is the same as that for source-free case
 
 ·The steady-state response is the final value of v(t). 
 Ø    vss(t) =  v(∞) 
 ·The values of A1 and A2 are obtained from the initial
 conditions:
 Ø    v(0) and dv(0)/dt. 
  
   
 
  
 
  
 
  
   
  
   
   
   
  
  
   
  
   
   
   
  
  
   
  
   
   
   
   
  
 (over-damped)
 
  
 (critically damped)
 
  
 (under-damped)