The OP AMP circuit shown in Figure P10-31 is purported to be a low-pass filter with a cutoff frequency at the single pole of the circuit and the dc gain given by the ratio of the two resistors.

(a) Find the input-output relationship \(V_{2}(s) / V_{1}(s)\).

(b) Select values of \(R_{1}, R_{2}\), and \(L\) so that the cutoff (the pole) is \(-1 \mathrm{krad} / \mathrm{s}\) and the gain is -10 .

(c) What is the gain of the circuit at \(s=0\) and \(\infty\) ? Does the filter function as described?