The circuit response in this case will contain exponentially-damped sinusoidal oscil-
lations. That is, the wave-shape of the natural response terms will be oscillatory with the
oscillation losing amplitude exponentially with time. The relevant expressions are derived
as below.
We define three new symbols – mainly for convenience at present. But they will turn
out to be important parameters in circuit studies soon. They are defined as below.
(11.6-6)
The roots of characteristic equation can be expressed in terms of these new symbols
as
Now we use Eqn. 11.6-4 for the zero-input response for v
C
(t) and substitute these
expressions for
α
1
and
α
2
and employ ...
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