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Q8. Determine the s-domain transfer function Consider the following \o...

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Q8. Determine the s-domain transfer function

Consider the following $\omega$ \omega domain transfer function

$H_f(\omega) = \frac{\omega}{8\omega + i(\omega^2 -15)}$ H_f(\omega) = \frac{\omega}{8\omega + i(\omega^2 -15)}

Convert this to the s-domain transfer function H_s(s).

$H_s(s) = \frac{1}{(s-3)(s+5)}$ H_s(s) = \frac{1}{(s-3)(s+5)}

❌

$H_s(s) = \frac{s}{s^2 + 15}$ H_s(s) = \frac{s}{s^2 + 15}

❌

$H_s(s) = \frac{-s^2}{(s+3)(s+5)}$ H_s(s) = \frac{-s^2}{(s+3)(s+5)}

❌

$H_s(s) = \frac{s}{(s+3)(s+5)}$ H_s(s) = \frac{s}{(s+3)(s+5)}

✅

$H_s(s) = \frac{s^2}{(s+3)(s-5)}$ H_s(s) = \frac{s^2}{(s+3)(s-5)}

❌

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