Let H $($jw$)=$jwRC$/1+$jwRC the Fourier Transform of the impulse response of an RC circuit and

x$($t$)=1+$cos $377$t $+$sin $377$t an input to that circuit.

$1.$Find X $($jw$)$the Fourier Transform of $($t$).(10$points$)$

$2.$Form the product X $($jw$)$H $($jw$)$the Fourier Transform of the output y$($t$).(10$points$)$

$3.$Find y$($t$)$the Inverse Fourier Transform of Y $($jw$).$Write it as y$($t$)=$A $+$Bcos$($wt $+$theta$)(10$points$)$

$4.$Find the RC product that makes the amplitude of ylt$)$equal to $(1)/($suare root of$2)$: $(10$points$)$