Electric Circuits and Networks, Ist Edition by Pearson

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 ...