Let H $($j$)=$ j$$RC$/1+$ j$$RC 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.

$$Find $($X j$)$ the Fourier Transform of x$($t$).(10$ points$)$

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

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

$4.$ Find the product that makes the amplitude of y$($t$)$ equal to $1/$root $2(10$ points$)$