$(25$ pts $)$ Consider the following circuit.

i$.$ Determine the transfer function of this circuit, $,$ notH$()!!).$

ii$.$ What kind of a filter is this circuit? Explain your reasoning.

iii. Assuming $R=62\mathrm{.}85$ and $L=0\mathrm{.}1H,$ calculate the break frequency of this circuit. $($Hint: Break frequency is where the magnitude of the transfer function is $\frac{1}{\sqrt[\phantom{2}]{2}}$ and the angle of the transfer function is $-45.)$

iv$.$ Assuming $R=62\mathrm{.}85$ and $L=0\mathrm{.}1H,$ find Vout$(t)$ for Vin$(t)=10cos(200t+30)$ using phasors.