$9-27.$ An OP$-$AMP circuit shown in Fig. P$9\mathrm{.}27$ has $R=10kQ$ and $C=10F.$ The relationship between the input and output of the OP$-$AMP is given by

$x_m=-0\mathrm{.}1\frac{d{v}_0(g)}{di}$

Figure P$2$:$27$ OP$-$AMP circuit for problicm P$9-27.$

$($a$)$ Suppose that the initial output voltage of the OP$-$AMP is zero. If an input voltage $v_{in}=-10sin(100r)V$ is applied to the OP$-$AMP circuit, integrate both sides of the equation given above to determine the voltage $v_o(n).$ Also, sketch the output voltage $v_d(t)$ for one cycle.

$($b$)$ Suppose that the instantancous power ahsorbed by the capacitor is $p(x)=sin(100n)-0\mathrm{.}5sin(200n)$ mw $,$ and that the initial stored energy is w$(0)=0.K-$omi$-$g that $p(t)=\frac{\text{d}\text{o}\text{e}\text{n}}{2},$ integrate both sides of the equation to determine the total stored emergy win.