$1.(2$ points$)$ Using the appropriate property from Problem $38,$ show that the Fourier transform of the zero$-$state response y$($t$)$ of the system to an arbitrary input f$($t$)$ is Y $($$)=$ H$($$)$F$($$),$ where Y $($$),$ H$($$),$ and F$($$)$ are the Fourier transforms of y$($t$),$ h$($t$),$ and f$($t$),$ respectively. The Fourier transform of the impulse response function h$($t$)$ is identical to the frequency response function H$($$)$ of the system. $2.(8$ points$)$ As a specific example, consider a LTIC system with the impulse response function h$($t$)=$ $2$ n d e $$nt sin$($dt$)$u$($t$),$ where n $>0,0$ $<1,$ and wd $=$ n p $1$ $2.$ By direct integration, determine the frequency response function of the system by computing the Fourier transform of the impulse response function. Express you answer in the standard form H$($$)=$ Y$$ F$=$ bm $($$)$ m $+$ bm$1($$)$ m$1+$ b$1($$)+$ b$0($$)$ n $+$ an$1($$)$ n$1+$a$1($$)+$ a$0.3.(5$ points$)$ Using the time differentiation property and the results from parts $1$ and $2,$ find the ODE representation of the system. Express your answer in the form d ny dtn $+$ an$1$ d n$1$y dtn$1++$ a$1$ dy dt $+$ aoy$($t$)=$ bm d mf dtm $+$ bm$1$ d m$1$f dtm$1++$ b$1$ df dt $+$ bof$($t$).$