Impulse Response / Frequency response

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Autra

Newbie level 1
I have a major question . Please take a look.

i have this de :

And i have to find IR and FR

We can "translate" the given de into:

Y(Ω)*(jΩ)^2 + Y(Ω)*5*(jΩ) + 4*Y(Ω)= jΩ*X(Ω)+2*X(Ω)

So i am reaching a point where H(Ω) = Y(Ω)/X(Ω) =

= (jΩ +2)/[(jΩ)^2 +5jΩ + 4] .

The my main problem is that i dont know how to continue from this point, because in the numerator is that jΩ, otherwise i have my standard methodology to solve it.

So what am i supposed to do for this point ?

Thanks

albert22

Full Member level 6
Aplying Laplace transform and solving for Y(s)/X(s) gives you the transfer function that is the same as the impulse response. Evaluating the transfer function for s=jw and taking magnitude and phase gives you the frequency response.
j^2 =-1
so
(jΩ +2)/[(jΩ)^2 +5jΩ + 4] = (jΩ +2)/[5jΩ + 4-Ω^2]
to get rid of a J you can normalize. That is multiply numerator and denominator by the conjugate.
Usually this is done to eliminate J in the denominator but you can do it in the numerator multipliying by
(jΩ -2)/(jΩ -2)

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