The name is absent



124


Solve the characteristic equation s2 + 2as + ωθ

Rj

LCRm


1 R1

O' — -———— -f∙ ---

2CRm 2L

-2a ± ʌ/4cv2 - 4ω2

^ 1

3~~2CRm


ʌʃɪ
2L V v 2CRm


-^1)2 _ /_!_ +

2L} yLC LCRm


Now sɪ and S2 are defined, along with ω0 the resonant frequency (in radians∕sec) and a the
damping factor

We look for a solution of the form υ(t) = K1es1t + K2es2t + K3

We need to solve for K1, K2 and K3 from the final and initial conditions

K1e~o° + K2e °° + K3 = is(R1∖∖Rm)

■ ⅛[K1e∙>< + ¾e∙=< + ¾] = ⅛∣ho = ≈√Cm

Kie0 + K2e0 + K3 = υ(0) = 0

K3 - ⅞ ( .Ri I ∣,Rto ) - is β11+‰

■ s1K1 + s2K2 = ^∖^ = is∣Cm

K1+ K2 = -K3

Now the system is fully defined



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