Consider an LTI system whose Frequency response is given in Eq$.(1).$

$Hj=\{\begin{array}{cc}2e^{-j2},& |w|<mn>5</mn><mn>0</mn>\\ 0& \text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

The input to the system is the signal $x(t)=10sin{c}^2(2t).$ By using the Fourier transform table $($pairs$/$properties$),$ whenever possible

$($a$)$ sketch the frequency response of the system

$($b$)$ sketch the Fourier transform of the output signal

$($c$)$ determine the energy of the output signal.