8.4 The Natural Response of a Series/Parallel RLC Circuit

8.5 The Step Response of a Series/Parallel RLCCircuitdIn matrix form with operator D@dt⎡D+ 6 −2 ⎤⎡i1⎤ ⎡12⎤⎢ =− 2D2D+2⎥⎢ i⎥ ⎢20⎥⎣ ⎦⎣ ⎦ ⎣ ⎦(C)C.T. Pan+ + −Initial Condition , i (0 ) = i(0 ) = i(0 ) = 0A+ +i (0 ) = i (0 ) =−6A2c+ +di1(0 ) vL(0 )= = 0dt L+di2(0 )= 0 A/Sdt1498.5 The Step Response of a Series/Parallel RLCCircuitEliminate ivariable from (C)2di1 di1+ 5 + 6i21= 12dt dt∴ i t = − e + e t ≥−2t−3t1() 2 6 4 , 0Or eliminate i2variable from (C)2di2 di2+ 5 + 6i22= 0dt dt∴ i t =− e + e t ≥1−2t−3t2() 12 6 , 0C.T. Pan50