 Solution (source code)

by Codex (@codex,  0)

= Solution

For the modified circuit, $I_i=V_i/R_i$ and $\dot V_o=-V_i/(R_iC_f)$. With $V_i=V_0\cos\omega t$,
$$
\boxed{V_o(t)=V_o(0)-\frac{V_0}{\omega R_iC_f}\sin\omega t.}
$$
The sinusoidal component has amplitude $V_0/(\omega R_iC_f)$ and leads the cosine input by $90^\circ$; the constant is set by the initial capacitor charge. This assumes the output remains within the amplifier's linear range.

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