6.4 Circuits Involving Two Energy Storage Elements cont.

Transient Behavior: Roots of the Characteristic Equation

p2 + ap + b = 0

Overdamped

Both roots will be negative and unequal so

xT(t) = A1e-a1t + A2e-a2t

Critically damped

Both roots will be negative and equal so

xT(t) = (A1 + A2t)e-at

Underdamped

Two complex conjugate roots (a ± jb) so

xT(t) = e-at[C1cos(bt) + C2sin(bt)]

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