Problem $(3)$: $20$ points. Consider the schematic on the right where the input VS is a step function going from $0$ to $10$ V at $\backslash ($ t$=0\backslash$mathrm$\{$sec$\}\backslash )$

$($A$)$ Write down the equation for V$1$ as a function of time. Evaluate V$1$ at $\backslash ($ t$=0\mathrm{.}5^\{*\}\backslash )$ RC

$($B$)$ Draw a normalized plot of V$1$ vs$.$ t using the graph given below.

$($C$)$ Replace the voltage step function Vs with a voltage sinewave function VS $($with a frequency of $60$ Hz $)$ and find the complex output V$1.$ Give the result in both rectangular and polar forms.