An \(R C\) series circuit is driven by the following periodic source:

\[
v_{\mathrm{s}}(t)=10 \cos 10 \mathrm{k} t+5 \cos 30 \mathrm{k} t+3.33 \cos 50 \mathrm{k} t \mathrm{~V}
\]

(a) Find the output taken across the capacitor when \(R=50\) \(\Omega\) and \(C=2 \mu \mathrm{F}\)

(b) Simulate the output using Multisim and compare it to the input when \(C\) varies from 0.1 to \(10 \mu \mathrm{F}\) Perform a "Parameter sweep" analysis on the capacitor over that range using a decade sweep, 2 points per decade. Comment on the output waveform, with respect to the input. What function is the circuit performing?