Finding amplitude and phase response of an amplifier

Question

I have a following problem, I have to find amplitude and phase response of an amplifier whose function is $$ H(s)={\frac {1}{s^2 + s + 100}} $$ I have solved simillar problems such as for this function $$ H(s)={\frac {1000s}{s + 10}}$$. Where I got $$ Ф(jw)=arctg(∞) - arctg(\frac{w}{10}) $$ and $$ 20log|H(jw)| = 20log100 + 20logw - 10log(1 + (\frac{w}{10})^2) $$

Does anyone know how to get amplitude and phase response for the first function?

Answer 1

First equate:$$ s = j\omega$$ then: $$s^{2} = -\omega^{2}$$ That gets rid of the squared term.

Then multiply top and bottom by the complex conjugate of the divisor and proceed as normal.