I have a simple transfer function, given by:
$$\frac{140,000}{s(s+100)}$$
I'm attempting to calculate the magnitude at $\omega$ = 100 rad/s.
So I plug in, I get $\frac{140,000}{20,000}$ = 7
Then I do $20log_{10}(7)$ = 16.9
Yet when I go through MATLAB, entering my transfer function and doing bode(sys), and then examining the point at w = 100, it tells me the magnitude there is 19.9.
I must be missing something stupid here...
Hint:
When calculation the magnitude, you can't just plug in the angular frequency into the transfer function. You first need to replace $s$ by $j\omega$ and then take the absolute value of the resulting expression.
$$\left|F(j\omega)\right|=\left|\frac{1400000}{j\omega(j\omega+100)}\right|=\frac{140000}{\omega |j\omega+100|}$$
Can you take it from here?