(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am given the transfer function H(s) = 10/(s(s^2 + 80s +400)) where s = jω [j is the imaginary unit i] and I am trying to get it into its magnitude and phase components.

3. The attempt at a solution

I rearranged it to 1/(40jω(1+ 4jω/20 + (jω/20)^2)) which is the standard form for transfer functions. I am wanting to plot the bode plots so I took the 20 * log base 10 of the entire transfer function and got for the magnitude: -20log(40) - 20log(1/(jω))- 20log(1+ 4jω/20 + (jω/20)^2)

and for the phase I got: -90° - tan^-1((ω/5)/(1-ω^2/400))

but in my textbook when they show the bode plots for the phase it has - tan^-1(ω/(1-ω^2/400)) for one of the phase factors and I am not sure why my numerator is ω/5 and there one is just ω.

If you don't study electrical engineering and are not sure of some of the stuff I said then basically H(s) = 10/(s(s^2 + 80s +400)) where s = jω is a complex number and j is the same as the imaginary unit i, so I need help to put this complex number into its magnitude and phase, I am pretty sure i got the magnitude part right.

Please can anyone help me by at least showing me how to get the phase part of this complex number

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# Magnitude and Phase of Transfer Function

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