Let $H(j)=\frac{jRC}{1+jRC}$ the Fourier Transform of the impulse response of an RC circuit and $x(t)=1+cos377t+sin377t$ an input to that circuit.

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

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

Find $y(t)$ the Inverse Fourier Transform of $Y(j).$ Write it as points$)$

Find the RC product that makes the amplitude of $y(t)$ equal to $\frac{1}{\sqrt[\phantom{2}]{2}}.(10$ points$)$

Hint: remember $f(x)(x-x_0)=f(x_0)(x-x_0)$

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