The complete response is written as the sum of the forced and the natural response, and the initial conditions are then determined and applied to the complete response to find the values of the constants

The over-damped response---- i()= A,+A, The critically-damped response-- i(t) =e (At+A2) The under-damped- response---it)e-(b1 cos+2 sino)

A1, A,----two arbitrary constants S S2----real numbers or conjugate complex Since the s,t and s,t must be dimensionless, S,, S2----(1/s)

The complete response of any RC circuit may also be obtained as the sum of the natural and the forced response

The complete response=the natural response+forced response

The series combination of a resistor and capacitor has a greater practical importance than does the combination of a resistor and an inductor

Let us assume a solution i(t=Ae, where a and S, are constant to be determined

We define the unit-step forcing function as a function which is zero for all values of argument which are less than zero and which is unity(1) for all positive values of its argument

4-5 Simple capacitor-OP-AMP-circuits Integrator op-amp circuit (Integrator):

Two circuits are dual if the mesh equations that characterize one of them have the same mathematical form as nodal equations that characterize the other