The OP AMP integrator in Figure P6-20 has (R=22) (mathrm{k} Omega, C=0.001 mu mathrm{F}), and (v_{mathrm{O}}(mathrm{o})=mathrm{o} mathrm{V}).

Question:

The OP AMP integrator in Figure P6-20 has $R=22$ $\mathrm{k} \Omega, C=0.001 \mu \mathrm{F}$, and $v_{\mathrm{O}}(\mathrm{o})=\mathrm{o} \mathrm{V}$. The input is $v_{\mathrm{S}}(t)=2 \sin$ $(\omega t) u(t) \mathrm{V}$. Derive an expression for $v_{\mathrm{O}}(t)$ and find the smallest allowable value of $\omega$ for linear operation of the OP AMP. Assume $V_{\mathrm{CC}}= \pm 15 \mathrm{~V}$.

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