PART II$-$RC Time Constants

$1.$ Construct the circuit shown below. The input is a $\backslash (50\backslash \%\backslash )$ duty cycle squarewave at $1$ kHz with a baseline of $0$ V and maximum value of $2\mathrm{.}5$ V $.$

$2.$ In your lab report derive an expression for the "charging" portion of the curve. $($You can assume that the charging starts at $\backslash ($ t$=0\backslash ).)$ Then derive an expression for the "discharging" portion of the curve. $($You can assume the discharging starts at $\backslash ($ t$=0\backslash ).)$

$3.$ Now increase the frequency of your input signal to $3$ kHz $.$ Explain what happens.