Frequency Response of an analog system?

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paulie walnuts

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An input of 2.δ(t) is applied to a system and produces the response

y(t)=6.e^-2t - 4.e^-3t

Find an expression for the systems frequency response.
 

I suppose that delta(t) is the Dirac impulse.
Then the impulse response is
h(t)=3*exp(-2*t)-2*exp(-3*t)
and the transfer function H(s) is its Laplace transform, thus
H(s)=3/(s+2)-2/(s+3)=(s+5)/(s^2+5*s+6).
Frequency response can be obtained after the substitution
s=jw.
 

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