Problem $4(25$ points$)$

A filter has the following differential equation.

$52$

$2+0\mathrm{.}3$

$+=()$

The input $()$ is the following:

$()=$ sin$(+30)+2$ cos $(0\mathrm{.}530)$

a$)$ Determine the Fourier Transform $()$ of the input.

b$)$ Determine the transfer function $()=()/()$

c$)$ Determine the Fourier Transform $()$

d$)$ Determine the steady$-$state waveform $()$ in the form

$()=$ cos$(+)+$ cos$(0\mathrm{.}5+)$