6.4 Circuits Involving Two Energy Storage Elements cont.
Ergo, -a ± jb = 0 ± j1 so that the prototype transient solution’s form: e-at[C1cos(bt) + C2sin(bt)] becomes: C1cos(t) + C2sin(t) \ v2,T(t) and iT(t) are: v2,T(t) = C1cos(t) + C2sin(t) and: iT(t) = C3cos(t) + C4sin(t)
The steady-state voltage and current are both nil since the LC circuit is source-free \
v2(t) = v2,T(t) = C1cos(t) + C2sin(t) and i(t) = iT(t) = C3cos(t) + C4sin(t)